Solve the following equation by factoring.

Question

A) x⁴-16x²+75=2x²-6

Answer 1

To solve the equation x⁴ - 16x² + 75 = 2x² - 6, we first need to combine like terms:

x⁴ - 16x² + 75 = 2x² - 6
x⁴ - 16x² - 2x² + 75 + 6 = 0
x⁴ - 18x² + 81 = 0

Now, we can factor this equation as a quadratic in terms of x²:

(x² - 9)(x² - 9) = 0
(x² - 9)² = 0

Now, taking the square root of both sides gives:

x² - 9 = 0
x² = 9
x = ±3

Therefore, the solutions to the equation x⁴ - 16x² + 75 = 2x² - 6 are x = 3 and x = -3.