If x^2= 1-3x, and without finding a value for x, show that x^4= 10 -33x

Answer 1

x^2 = 1 -3x

square both sides to get

x^4 = 1 - 6x + 9x^2

substitute 1-3x for x^2 on the right side

=1 -6x + 9(1-3x)

= 1 -6x + 9 -27x

combine like terms

= 10 -33x