Question

(x^2-1)^3=64(X^2-1)^2

Answer 1

x = ±1, ±√65

Explanation:

You want the solution to (x² -1)³ = 64(x² -1)².

Solution

Subtracting the right side, we have ...

(x² -1)³ -64(x² -1) = 0

(x² -1)²(x² -1 -64) = 0

Zero product rule

The solutions make the factors zero:

x² -1 = 0 ⇒ x = ±1

x² -65 = 0 ⇒ x = ±√65

Solutions are x = ±1 and x = ±√65.

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Additional comment

The solutions ±1 are each multiplicity 2.