Question

if x= 1/4-x .. find the value of x ^6 + x^6+ 1/x^6

Answer 1

x = 1/( 4 - x )

x( 4 - x) = 1

4x -x² = 1

1 +x² = 4x

divided by x

1/x + x = 4

x + 1/x = 4
so,
x² + 1/x² = (x +1/x)²-2x.1/x = (4)² -2 = 14

now,
x^6 + 1/x^6 = (x² + 1/x²)³ -3( x² + 1/x²)
=( 14)³ -3( 14)
=14( 196 -3)
=14× 193
=2702