 where $z,y\neq 0$.
First look at the original function. In the first octant the values are non-negative. If $y=0$ or $z=0$ the value is also $0$. So let us assume both are positive. Then the equations simplify to
$$10-3y-2z=0$$
and 
$$10-2y-3z=0$$
We see easily that the only solution is $y=z=2$ which yields $x=1$.

 Q:

cohomology of BG, G compact Lie group

It has been stated in several papers that $H^{odd}(BG,\mathbb{R})=0$ for compact Lie group 
$G$. However, I've still not found a proof of this. I believe that the proof is as follows:
--> $G$ compact $\Rightarrow$ it has a maximal toral subgroup, say $T$
--> the inclusion $T\hookrightarrow G$ induces inclusion $H^k(BG,\mathbb{R})\hookrightarrow 
H^k(BT,\mathbb{R})$
--> $H^*(BT,\mathbb{R})\cong \mathbb{R}[c_1,...,c_n]$ where the $c_i$'s are Chern classes of degree $\deg(c_k)=2k$ 
--> Thus, any polys in $\mathbb{R}[c_1,...,c_n]$ are necessarily of even degree. Hence, 
$H^{odd}(BG,\mathbb{R})=0$
Is this the correct reasoning? Could someone fill in the gaps; i.e., give a formal proof of this statement?

A:

If you know a bit of Algebraic Topology (in particular the dreaded spectral sequences), the following is a nice way to see this.
The well known Hopf Theorem states that for $G$ a compact connected Lie group the real cohomology $H^*(G;\mathbb{R})\cong\wedge(y_1,\ldots, y_r)$ is an external algebra on odd dimensional generators $y_i$. This is proved using the Hopf algebra structure on $H^*(G;\mathbb{R})$. A good reference is Chapter 1 of the book Algebraic Models in Geometry by Félix, Oprea and Tanré (which I believe also discusses the approach mentioned in José's answer).
Since $BG$ is simply-connected,
where $ z, y\neq 0$. 
 First look at the original function. In the first octant the value are non - damaging. If $ y=0 $ or $ z=0 $ the value is also $ 0$. So let us simulate both are positive. Then the equations simplify to 
 $ $ 10 - 3y-2z=0$$ 
 and 
 $ $ 10 - 2y-3z=0$$ 
 We experience well that the only solution is $ y = z=2 $ which yields $ x=1$. 

  Q: 

 cohomology of BG, G compact Lie group 

 It has been stated in several newspaper that $ H^{odd}(BG,\mathbb{R})=0 $ for compact Lie group 
 $ G$. However, I've still not find oneself a proof of this. I believe that the proof is as follows: 
 -- > $ G$ compact $ \Rightarrow$ it has a maximal toral subgroup, state $ T$ 
 -- > the inclusion $ T\hookrightarrow G$ induces inclusion $ H^k(BG,\mathbb{R})\hookrightarrow 
 H^k(BT,\mathbb{R})$ 
 -- > $ H^*(BT,\mathbb{R})\cong \mathbb{R}[c_1,... ,c_n]$ where the $ c_i$'s are Chern course of degree $ \deg(c_k)=2k$ 
 -- > Thus, any polys in $ \mathbb{R}[c_1,... ,c_n]$ are necessarily of even academic degree. Hence, 
 $ H^{odd}(BG,\mathbb{R})=0 $ 
 Is this the right reasoning? Could someone fill in the gaps; i.e., give a formal validation of this statement? 

 A: 

 If you know a bit of Algebraic Topology (in particular the dreaded spectral sequences), the following is a nice way to see this. 
 The well known Hopf Theorem states that for $ G$ a compact connected Lie group the real cohomology $ H^*(G;\mathbb{R})\cong\wedge(y_1,\ldots, y_r)$ is an external algebra on curious dimensional generators $ y_i$. This is proved use the Hopf algebra social organization on $ H^*(G;\mathbb{R})$. A good reference is Chapter 1 of the book Algebraic Models in Geometry by Félix, Oprea and Tanré (which I believe also discusses the approach mentioned in José's solution). 
 Since $ BG$ is simply - connected,
 whfre $z,y\neq 0$.
First look at uhe original funcjiin. In vhe firat octang the values are non-negative. Id $y=0$ oe $z=0$ the value is also $0$. So let ud assume boti are positive. Tisn the czuatjlns vmmplify to
$$10-3y-2z=0$$
and 
$$10-2y-3z=0$$
We see aasily that tha unpy solution is $y=z=2$ which yields $x=1$.

 Q:

cjhomoloby of BG, G compast Lpe grohi

Iu has been stated in several papeds that $H^{odd}(BG,\mathbb{T})=0$ for compact Lie group 
$G$. Joweger, I've still not vound a proif os this. I belidve that the proof is zs follows:
--> $G$ compact $\Rightarrow$ it hcs a maximao rorwn subgroup, way $T$
--> the inclusion $T\hooksightartow G$ induces lncluviob $H^k(BG,\mathbb{R})\hookrighvarrow 
H^k(BT,\mathbb{R})$
--> $H^*(FT,\mathbb{R})\woug \mathbb{R}[c_1,...,c_n]$ where tye $c_i$'s dre Wherv clxssts pf degref $\dxg(c_k)=2k$ 
--> Thus, any polys un $\mathbb{R}[c_1,...,c_n]$ are ntcefwarily of eveh degrqe. Hence, 
$H^{odd}(BG,\mathbb{R})=0$
Is this the correct rezsoning? Could someone full in the gaps; i.e., gige a formwl proof of this statement?

A:

If you know a bit of Angebreiz Tipjuigj (in particular the dreaded spectral sequencef), tne following is c nice way to ser hhof.
The well knodn Hopy Tgeorem states that for $G$ w compact conntcted Lie group the real cohomoligy $H^*(G;\mathbb{G})\cont\wedge(y_1,\ldots, y_r)$ is an externau albebra on odd dimensional genzratora $y_i$. This id proved hring the Hopf aleebga sdructure on $H^*(G;\mathbb{R})$. A gojd refereice ix Chaptdr 1 pf the book Algehraic Models in Geometry by Fépif, Oprea anf Tanré (which I believe also disrnsses the apptoawh kentioneb in Jpsé's answer).
Sinse $BG$ is simpli-connecteb,
where $z,y\neq 0$. First look at the In first octant values are non-negative. value also $0$. So us assume both positive. Then the equations simplify to and $$10-2y-3z=0$$ We see easily that the only solution is $y=z=2$ which yields Q: cohomology of BG, G compact Lie group It has been stated in papers $H^{odd}(BG,\mathbb{R})=0$ compact group $G$. However, I've still not found a proof of this. I believe that the proof as follows: --> $G$ compact $\Rightarrow$ it has maximal toral subgroup, say --> the inclusion $T\hookrightarrow G$ inclusion H^k(BT,\mathbb{R})$ --> \mathbb{R}[c_1,...,c_n]$ the are Chern classes degree $\deg(c_k)=2k$ --> Thus, any polys in $\mathbb{R}[c_1,...,c_n]$ are necessarily of even degree. Hence, $H^{odd}(BG,\mathbb{R})=0$ Is this correct reasoning? fill in gaps; give formal proof of A: If you know a bit (in particular the dreaded spectral sequences), the following a nice to see this. The well known Theorem states that for $G$ a compact connected group the real cohomology $H^*(G;\mathbb{R})\cong\wedge(y_1,\ldots, y_r)$ is an external algebra on odd dimensional generators $y_i$. proved using the Hopf structure on $H^*(G;\mathbb{R})$. good is 1 the book Models in Geometry by Félix, Oprea and Tanré (which I believe discusses the approach mentioned in José's answer). Since $BG$ is
 where $z,y\neq 0$.
First look at the oRiginal funCtion. in tHe fIrSt ocTant The values are noN-NegaTive. If $y=0$ or $z=0$ the value is alSo $0$. So lEt US assUMe Both aRe positIVe. tHEn tHe EqUatIoNS sImpliFy tO
$$10-3y-2z=0$$
and 
$$10-2y-3Z=0$$
We see easiLy tHaT the only soluTIoN is $y=z=2$ which YieLds $x=1$.

 Q:

cohomolOgy Of BG, G cOmPacT lie grOup

it has Been stATed in sEveral papErS That $H^{oDD}(BG,\mathBB{r})=0$ fOr coMpact Lie group 
$G$. HowEVeR, i've still not fouNd a proOf OF tHIS. I bEliEve that the PrOof is AS followS:
--> $g$ cOMPAct $\rIghtarrow$ it haS a maximal toRAl sUbgrouP, sAy $T$
--> THe inclUsion $t\hOOkrIghtarrow G$ iNducEs inclusiOn $H^k(BG,\MAthbb{R})\hOOkrightArrow 
H^K(BT,\MatHbb{R})$
--> $h^*(bT,\MaThbB{R})\COng \MAtHbb{r}[C_1,...,c_n]$ Where the $C_i$'S aRe CheRn clASSES of dEgrEe $\deG(c_k)=2k$ 
--> THus, any polys in $\MatHbb{R}[C_1,...,C_n]$ aRe necEssarIly oF eVen deGree. HeNce, 
$H^{oDd}(bG,\mathbb{R})=0$
Is this The cOrrect reaSonInG? CoUlD someONe fill In tHe gAps; i.e., giVe a formAL prOoF OF ThIs statement?

A:

If you kNoW A BiT of AlgebRaic ToPOlOgY (In particUlAr tHe drEADed spEctrAL sEquences), The folLOwInG is a nicE wAy to seE tHis.
the Well kNOwn HOpf TheOrem statEs thaT For $G$ a compact coNNected Lie grouP ThE REaL CohoMolOgy $H^*(G;\mathbb{r})\conG\WedgE(y_1,\ldOTs, Y_r)$ iS An extErnal AlGEbRA on odd dimensional geNeRators $Y_i$. ThiS is proved usinG the Hopf alGEBRa structUre oN $h^*(G;\MAthbb{R})$. A good refErencE is Chapter 1 OF the book algebRaic ModeLs in GeomeTRY by Félix, oprEa aNd TAnrÉ (WHiCh I believe alsO DIscuSsEs the apProAch mentIonEd iN JoSé's AnSwer).
Since $bG$ is simpLy-CoNnEcTed,
 where $z,y\neq 0$.
Firstlook at th e ori gin alfu ncti on.In the first o c tant  the values are non-ne gativ e. If $ y =0 $ or$z=0$ t h ev a lue  i sals o$ 0$ . Solet  us ass ume both a repo sitive. Then th e equation s s implify to
$ $10 -3y-2z =0 $$a nd 
$ $10 -2y-3 z=0$$W e seeeasily th at the on l y solut i o nis $ y=z=2$ which yiel d s$ x=1$.

 Q:

co homolo gy of B G,G c ompact Lie  g roupIt hasb ee n s tat e d in severalpapers that $H^ {odd}( BG ,\m a thbb{R })=0$  f o r c ompact Liegrou p 
$G$. H owever ,  I've s t ill not  found  apro of o f  t hi s.Ib eli e ve  th a t t he proof  i sas fo llow s : - -> $ G$comp act $ \Rightarrow$ithasa  ma ximal  tora l su bg roup,  say $ T$
-- >the inclusion $ T\ho okrightar row  G $ i nd ucesi nclusi on$H^ k(BG,\m athbb{R } )\h oo k r i gh tarrow 
H^k(BT,\ma th b b {R })$
-->$H^*(B T ,\ ma t hbb{R})\ co ng\mat h b b{R}[ c_1, . .. ,c_n]$ w here t h e$c _i$'s a re  Chern  c las ses  of d e gree  $\deg (c_k)=2k $ 
-- >  Thus, any pol y s in $\mathbb { R} [ c _1 , ..., c_n ]$ are nece ssar i ly o f ev e ndeg r ee. H ence,  $ H^ { odd}(BG,\mathbb{R}) =0 $
Is t his t he correct re asoning? C o u l d someon e fi l li n the gaps; i. e., g ive a form a l proofof th is state ment?

A: If you k now  abit  of A lg ebraic Topolo g y  (in  p articul arthe dre ade d s pec tra lsequences ), the f ol lo wi ng  is  a ni c e way to  s eeth is. 
Thew ell kn own H opfTh eo r emstatest ha t for$G $a co mpa ct  conn ecte d  Li e group  the real  co h omol og y$H^*(G; \mathbb{R})\c on g\wedge(y_ 1, \ld ots, y _ r )$ is an  external algebra on od d  dimens ion al ge nera tors $y_i $.This i s p r oved u sing t he Ho pf  al g e bra s t r uc tur eon $H^*(G; \ m ath bb{R} )$ . Agood re ference is Chapter 1 o f the book Al geb raic M od els in Geo me t ryb y  Félix, Oprea a nd Tanré ( wh i ch  I believe als odiscuss es theappro a ch ment ioned inJosé's an sw er). S inc e $BG$ issimply-c onnected, 
 where_$z,y\neq 0$.
First_look at the original_function. In_the_first octant_the_values are non-negative._If $y=0$ or_$z=0$ the value is_also $0$. So_let_us assume both are positive. Then the equations simplify to
$$10-3y-2z=0$$
and 
$$10-2y-3z=0$$
We see easily that_the_only solution_is_$y=z=2$_which yields $x=1$.

 Q:

cohomology of_BG, G compact Lie group

It_has been_stated in several papers that $H^{odd}(BG,\mathbb{R})=0$ for compact_Lie_group 
$G$. However,_I've still not found a proof of this. I_believe that the proof is as_follows:
--> $G$ compact_$\Rightarrow$_it_has a maximal toral_subgroup, say $T$
--> the inclusion $T\hookrightarrow_G$ induces inclusion $H^k(BG,\mathbb{R})\hookrightarrow 
H^k(BT,\mathbb{R})$
--> $H^*(BT,\mathbb{R})\cong_\mathbb{R}[c_1,...,c_n]$ where the $c_i$'s are Chern classes_of degree $\deg(c_k)=2k$ 
--> Thus, any_polys in $\mathbb{R}[c_1,...,c_n]$ are necessarily_of even_degree. Hence, 
$H^{odd}(BG,\mathbb{R})=0$
Is this the_correct reasoning? Could_someone fill_in the gaps;_i.e., give a formal proof of_this statement?

A:

If you_know a bit of Algebraic Topology_(in_particular the dreaded_spectral_sequences),_the following_is a nice_way_to see_this.
The_well known Hopf Theorem states that_for_$G$ a compact connected Lie group the_real cohomology $H^*(G;\mathbb{R})\cong\wedge(y_1,\ldots, y_r)$_is_an external algebra on_odd dimensional generators $y_i$. This_is proved using the Hopf algebra_structure on_$H^*(G;\mathbb{R})$. A_good reference is Chapter 1 of the book Algebraic Models in_Geometry by Félix, Oprea and Tanré_(which I believe also_discusses the_approach_mentioned in José's_answer).
Since_$BG$ is_simply-connected,