Question

x^4 - 8x^2 = -1
is my first step to square both sides? if so then whats' the next step?

Answer 1

Let x² = u; u² - 8u = -1

Now add both sides by 16.

u² - 8u + 16 = 15

(u - 4)² = 15

u - 4 = ±√15

u = 4 ± √15

x² = 4 ± √15

\(x = \pm\sqrt{4\pm\sqrt{15}}\)

\(\boxed{x = \sqrt{4+\sqrt{15}}~\text{or}~\sqrt{4-\sqrt{15}}~\text{or}~-\sqrt{4+\sqrt{15}}~\text{or}~-\sqrt{4-\sqrt{15}}}\)

Answer 2

oh okay, i would not have thought of that one. thanks