# If |x^2-2x+2|-|2x^2-5x+2|=|x^2-3x| then the set of values of x is

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(-oo , 0] cup [ 3,00)[0,1/2] cup [2,3](-oo,0]cup [1/2,2] cup [3,oo)[0,2] cup [3,oo)

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Solution :
We have, <br> |2x^(2)-5x+2|+|x^(2)-3x|=|x^(2)-2x+2| = |(2x^(2)-5x+2)-(x^(2)-3x)| <br> therefore (2x^(2)-5x+2) (x^(2)-3x) le 0 <br> rArr (2x-1) (x-2) x (x-3) le 0 <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CEN_ALG_C01_E06_029_S01.png" width="80%"> <br> From the sign scheme, we have x in[0,(1)/(2)]cup [2,3] Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams. Transcript

friends at today's question is if Mod of x square - 2 X + 2 - Mod of 2 x square - 5 x + 2 equal to x square Mod of x square then we will have to calculate the values of X so here are some options are given to us now for solving this question what will do solution part what we will do we will take this to write inside so this will become Mod of x square - 2 x 2 equal to MOD of 2 x square - 5 x + 2 + Mod of x square - 3 x so what we do now we will write a test model 2 x square - 5 x + 2 x square

- 3 x Mod that is equal to MOD of 2 x square - 5 x + 2 + Mod of x square - 3 now what we will do now from here we can conclude that as this are getting subtracted and desired getting added but there deputed equal so from here what we can conclude or we can say we are going to use a property liya what property we are going to use we are going to use this property the property that is what if Mod of x minus y equal to MOD of X + Mod of X + Mod of Y then we can write it is x then we can write xy is less than or equal to zero this we are going to use hair so what we will do this X this will

be less than or equal to zero so this will be 2 x square - 5 x + 2 x x square - 3 x is less than or equal to zero what we will get to x minus 2 x x minus 2 x x x x minus 3 x and find the roots of hair roots of this year so we will get this less than equal to zero now we are going to use Wavy curve method show on number line we will write this numbers so first is zero half 2 and 3 so now what we can confirm if the number is great if the value of x is greater than 3 then the value of this will be positive so it will be positive after three thus I will be changed to negative than positive the

negative and positive and we can also take the value is equal to zero to we will include this values to two now we have to take less than or equal to zero values less than equal to zero so we will take this values here the value of this will be less than or equal to zero so the value of x X belongs to close bracket zero to half Union close bracket 223 so this is our answer the value of x now the ok let's see the option which option is correct so we got the values 0 to have and 223 so the option 20 correct so answer is SBI open

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