What are the solutions of the equation x4 - 9x2 + 8 = 0? Use u substitution to solve. x = 1 and x = 2 StartRoot 2 EndRoot x = ±1 and x = plus-or-minus 2 StartRoot 2 EndRoot x = ±i and x = plus-or-minus 2 i StartRoot 2 EndRoot x = ±i and x = 2 StartRoot 2 EndRoot

The solutions are

x = - 1, 1, - 2√2, and 2√2.

Step-by-step explanation:

Given the equation

x^4 - 9x² + 8 = 0

Let u = x², then the equation becomes

u² - 9u + 8 = 0

u² - u - 8u + 8 = 0

(u² - u) - (8u - 8u) = 0

u (u - 1) - 8 (u - 1) = 0

(u - 8) (u - 1) = 0

u - 8 = 0

=> u = 8

Or

u - 1 = 0

=> u = 1

For u = 8

=> x² = 8

=> x = ±√8 = ±2√2

For u = 1

=> x² = 1

=> x = ±√1 = ± 1