solve the equation. 1296x^-4 - 97x^-2+1=0?

Question

express answer in simplified form.

pre cal.

Answer 1

1296x^-4 - 97x^-2+1=0
Multiply both sides of the equation by x^4:
1296 – 97 x^2 + x^4 = 0
Just rewrite to usual form:
x^4 – 97 x^2 + 1296= 0
Substitute y=x^2:
y^2 – 97 y + 1296= 0
That is a simple quadratic equation. Solutions are:
y = 81
and
y=16.
Now solve for x. To every value of y we get two values of x. All four solutions of the original equation are:
x = 9, x = -9, x = 4, and x = -4.
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