Solve the equation after making an appropriate substitution.

Question

x⁴-16x²+63=0

Determine the appropriate substitution using the new variable u.

Answer 1

u=x^2

u^2 -16u + 63 = 0

u^2 -16u + 64 =-63+64

(u-8)^2 = 1

u -8 = + or -1

u = 9 or 7

u = x^2 = 9 or 7

x = + or - sqr9 or + or - sqr7

x = +3 or +sqr7