SOLUTION: Solve the equation by introducing a substituition that transforms this equation to quadratic form. x^-8-17x^-4+16=0

Question 210917: Solve the equation by introducing a substituition that transforms this equation to quadratic form.
x^-8-17x^-4+16=0
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
x^-8-17x^-4+16=0
.
Let t = x^-4
now, substitute the above into the original:
t^2 - 17t + 16 = 0
(t-16)(t-1) = 0
t = {1, 16}
.
To find x, use the fact that t=x^-4
1 = x^-4
1 = 1/x^4
x = 1
.
16 = x^-4
16 = 1/x^4
x^4 = 1/16
x = 1/2
.
x = +-{1, 1/2}

RELATED QUESTIONS
Solve the equation by introducing a substituition that transforms this equation to... (answered by nerdybill)

Solve by introducing a substitution that transforms these equations to quadratic form... (answered by Fombitz)

Solve the equation by introducing a substitution that transforms these equations to... (answered by josgarithmetic)

Solve the equation by introducing a substitution that transforms this equation into... (answered by ewatrrr,josgarithmetic)

Solve the equation by introducing a substitution that transforms this equation to... (answered by Fombitz)

Struggling on this end. I am supposed to solve by introducing a substitution that... (answered by NYC Math Tutor,drj)

solve the equation by making a substituition x-(7*x^.5)+8... (answered by 303795)

Please help me solve this equation: {{{ x^4-17x^2+16=0... (answered by backback,jim_thompson5910)

How do you solve this quadratic equation??? x squared... (answered by Greenfinch,Theo)