What are the solutions of the equation 9x⁴ - 2x² - 7 = 0? use u-substitution to solve.

Solution:

Using the substitution rule we put x² = u .

The given equation now changes to

9u² - 2u - 7 = 0 --- (1)

Equation(1) is a simple quadratic equation which can be solved by factorization as follows:

9u² - 2u - 7 = 0

(9u + 7)(u - 1) = 0

Therefore

9u + 7 = 0 → u = -7/9

u -1 = 0→ u = 1

Since u = x² implies

x = √-7/9 = ± i√7/9

x = √1 = ± 1

What are the solutions of the equation 9x⁴ - 2x² - 7 = 0? use u-substitution to solve.

Summary:

The solutions of the equation 9x⁴ - 2x² - 7 = 0 using u-substitution method are x = ± i√7/9; x = ±1.