AP EAMCET20226 Jul 2022Evening ShiftMathematicsQuadratic EquationActual

The sum of squares of roots of the equation x^ 2 3 +x^ 1 3 -2=0 is

Options

Correct answer

B. 65

Step-by-step solution

Given, equation is array rlrl & & x^ 2 / 3 +x^ 1 / 3 -2 & =0 & & x^ 2 / 3 +x^ 1 / 3 & =2 & & (x^ 2 / 3 +x^ 1 / 3 )^3 & =2^3 & & & [ (a+b)^3 . & .=a^3+b^3+3 a b(a+b) ] array aligned & x^2+x+3 x 2=8 & x^2+7 x-8=0 & (x+8)(x-1)=0 x=1 ;-8 & Sum of square roots =(1)^2+(-8)^2 & =1+64=65 aligned

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