AP EAMCET202317 May 2023Evening ShiftMathematicsQuadratic EquationActual

If and are the roots of the equation 2^ 6 x -3 (2^ 3 x+2 )+32=0 with < 1 , then 2 +3 =

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Correct answer

D. 4

Step-by-step solution

Since, 2^ 6 x -3 (2^ 3 x+2 )+32=0 aligned & (2^ 3 x )^2-12 (2^ 3 x )+32=0 & Let y=2^ 3 x & y^2-12 y+32=0 & (y-4)(y-8)=0 & y=4 or, y=8 & 2^ 3 x =4 or, 2^ 3 x =8 & 2^ 3 x =22 or, 2^ 3 x =23 aligned x= 2 3 or, x=1 Hence, =1 & = 2 3 Then, 2 +3 =2 1+3 2 3 =4

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