Question

Which of the following is an extraneous solution of (45-3x)² = x-9?

Ox=-12
O x = -3
O x = 3
O x = 12

Answer 1

To find the extraneous solutions of the equation (45-3x)² = x-9, we solve the equation and check if any of the solutions make the equation false. The only extraneous solution is x = -3.69.

Step-by-step explanation:

To find the extraneous solutions of the equation (45-3x)² = x-9, we need to solve the equation and check if any of the solutions make the equation false. Let's solve it:

(45-3x)² = x-9

2025 - 270x + 9x² = x - 9

9x² - 271x + 2034 = 0

We can solve this quadratic equation using factoring, completing the square, or the quadratic formula. After solving, we find that x is approximately -3.689 or 24.333. Therefore, the only extraneous solution is x = -3.69.

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