Answer: x = ±1 and x = ±2.
Step-by-step explanation:To solve the equation (5x^2 - 4)^(1/4) = x, follow these steps:
Raise both sides of the equation to the fourth power to eliminate the fourth root:
((5x^2 - 4)^(1/4))^4 = x^4
Simplify both sides:
5x^2 - 4 = x^4
Rearrange the equation into a standard polynomial form:
x^4 - 5x^2 + 4 = 0
Factor the polynomial:
(x^2 - 1)(x^2 - 4) = 0
Solve each factor separately:
For x^2 - 1 = 0:
x^2 = 1
x = ±1
For x^2 - 4 = 0:
x^2 = 4
x = ±2
So, the solutions for the equation are x = ±1 and x = ±2.
