<prompt> Pata idadi ya masuluhisho halisi x,y,z,w ya milinganyo ya wakati mmojaanzaalignMiaka 2 x frac17x, 2z y frac17y, 2w z frac17z, 2x w frac17w.mwishopanga  <response>: Kwa ukaguzi, sqrt17,sqrt17,sqrt17,sqrt17 na -sqrt17,-sqrt17,-sqrt 17,-sqrt17 ni suluhisho. Tunadai kuwa haya ndiyo masuluhisho pekee.Hebufx frac12 kushoto x frac17x kulia fracx2 172x.Kisha kilichotolewa milinganyo huwa fx y, fy z, fz w, na fw x. Kumbuka kwamba hakuna mojawapo ya vigeu hivi inayoweza kuwa 0.Tuseme t 0. Kishaft - sqrt17 fract2 172t - sqrt17 fract2 - 2t sqrt17 172t fract - sqrt1722t ge 0,so ft ge sqrt17. Kwa hivyo, ikiwa yoyote kati ya x, y, z, w ni chanya, basi zote ni chanya, na kubwa kuliko au sawa na sqrt17.Zaidi ya hayo, ikiwa t sqrt17, basift - sqrt17 fract - sqrt1722t frac12 cdot fract - sqrt 17t t - sqrt17 frac12 t - sqrt17.Kwa hivyo, ikiwa x sqrt17, basianzaaligny - sqrt17 frac12 x - sqrt17, z - sqrt17 frac12 y - sqrt17, w - sqrt17 frac12 z - sqrt17, x - sqrt17 frac12 w - sqrt17.mwishoalignHii inamaanishax - sqrt17 frac12 w - sqrt17 frac14 z - sqrt17 frac1 8 y - sqrt17 frac116 x - sqrt17,kinzani.Kwa hivyo, sqrt17,sqrt17,sqrt17,sqrt17 ndio suluhisho pekee ambapo viambajengo vyovyote ni chanya.Ikiwa vigezo vyovyote ni hasi, basi vyote ni hasi. Acha x -x, y -y, z -z, na w -w. KishaanzaalignMiaka 2 x frac17x, 2z y frac17y, 2w z frac17z, 2x w frac17w,endalignna x, y, z, w zote ni chanya, ambayo ina maana x,y,z,w sqrt 17,sqrt17,sqrt17,sqrt17, hivyo x,y,z,w -sqrt17,-sqrt17 ,-sqrt17,-sqrt17.Kwa hivyo, kuna 2 suluhisho. 