Question

Solve x4 – 17x2 16 = 0. let u = ✔ x² . rewrite the equation in terms of u. ✔ u² - 17u 16 = 0 factor. ✔ (u - 16)(u - 1) = 0 select all of the solutions to the original equation.

a.(u-16)(u+1)=0
b.(u-16)(u-1)=0
c.(u+16)(u-1)=0
d.(u+16)(u+1)=0

Answer 1

The equation is factored to (u - 16)(u - 1) = 0 after substituting u for x², and upon reverting the substitution, the solutions for x are determined as 4, -4, 1, and -1.

Step-by-step explanation:

To solve the equation x4 − 17x2 + 16 = 0, we first let u = √ x², which is equivalent to u = x2. This substitution simplifies the equation to u2 − 17u + 16 = 0, a quadratic equation in terms of u. We then factor the quadratic equation, which gives us (u - 16)(u - 1) = 0. Setting each factor equal to zero, we find that u can be either 16 or 1. To find the solutions for x, we reverse the substitution, leading to x2 = 16 and x2 = 1, respectively. Solving these equations yields four possible solutions for x: x = 4, x = -4, x = 1, and x = -1.