AP EAMCET202316 May 2023Morning ShiftMathematicsQuadratic EquationActual

If and are the roots of the equation 2 x^2-4 x+3=0 , then 2 ( ^4+ ^4 )+3 ( ^2+ ^2 ) + =

Options

Correct answer

B. -2

Step-by-step solution

and are roots of 2 x^2-4 x+3=0 + = -(-4) 2 =2 and = 3 2 ^2+ ^2=( + )^2-2 =4-2 3 2 =1 ( ^2+ ^2 )^2= ^4+ ^4+2 ^2 ^2 1= ^4+ ^4+2 ( 3 2 )^2 ^4+ ^4=1- 9 2 ^4+ ^4=- 7 2 Now, 2 ( ^4+ ^4 )+3 ( ^2+ ^2 ) + = 2 (- 7 2 )+3 1 2 = -7+3 2 = -4 2 2 ( ^4+ ^4 )+3 ( ^2+ ^2 ) + =-2

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