Solve the equation

Question

Solve x^4-8x^2+16=0

Answer 1

x^4 - 8x^2 + 16   =   0

(x^2)^2 - 8(x^2) + 16   =   0

Substitute x^2 = y in above equation

y^2 - 8y + 16   =   0

y^2 - 4y - 4y + 16   =   0

y(y - 4) - 4(y - 4)   =   0

(y - 4) (y - 4)   =   0

(y - 4)^2   =   0

y - 4   =   0

y  =  4

x^2   =   4             [ Since y  =  x^2 ]

Apply square root on each side

x  =  2

The solution is x = 2.