JEE Main20249 Apr 2024Morning ShiftMathematicsQuadratic EquationActual
Let , be the roots of the equation x^2+2 2 x-1=0 . The quadratic equation, whose roots are ^4+ ^4 and 1 10 ( ^6+ ^6 ) , is :
Options
- Ax^2-190 x+9466=0
- Bx^2-180 x+9506=0
- Cx^2-195 x+9506=0
- Dx^2-195 x+9466=0
Correct answer
C. x^2-195 x+9506=0
Step-by-step solution
aligned & x^2+2 2 x-1=0 & + =-2 2 & =-1 & ^4+ ^4= ( ^2+ ^2 )^2-2 ^2 ^2 & = (( + )^2-2 )^2-2( )^2 & =(8+2)^2-2(-1)^2 & =100-2=98 & ^6+ ^6= ( ^3+ ^3 )^2-2 ^3 ^3 & = (( + ) (( + )^2-3 )^2-2( )^3 . aligned aligned & =(-2 2 (8+3))^2+2 & =(8)(121)+2=970 & 1 10 ( ^6+ ^6 )=97 & x^2-(98+97) x+(98)(97)=0 & x^2-195 x+9506=0 aligned