x^4-22x^2+96=0

Question

solve the equation after making an appropriate substitution x^4-22x^2+96=0

Answer 1

This equation factors.

x⁴ - 22x² + 96=0

(x² - 16)(x² - 6) = 0

x² = 16 or 6

x = ±4 or ±√6

Answer 2

You could make a substitution u = x²

You can rewrite x⁴ - 22x² + 96 = 0 as

(x²)² - 22(x²) + 96 = 0 which makes it easier to see where to make the substitution:

u² - 22u + 96 = 0

now factor it by finding two numbers which multiply to equal 96, and add up to -22: (-6)*(-16) = 96 and (-6) + (-16) = -22

(u - 16)(u - 6) = 0

u = 16 or u = 6. Remember that u = x² and now you can solve it as Roman did.