Question

X-2

Which solution to the equation x-1 2x²-2 is extraneous?
O x = 1 and x = -4
neither x = 1 or x = -4
O x = 1
O x = -4
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Answer 1

To find the extraneous solution, we solve the equation and check if any solution doesn't satisfy the original equation. The extraneous solution for the given equation x-1 = 2x²-2 is x = -1/2.

Step-by-step explanation:

The given equation is x-1 = 2x²-2. To find the extraneous solution, we need to solve the equation and check if any solution doesn't satisfy the original equation. Let's solve the equation:

x - 1 = 2x² - 2

Moving all terms to one side, we get:

2x² - x - 1 = 0

We can solve this equation by factoring or using the quadratic formula. Factoring the quadratic equation, we get:

(2x + 1)(x - 1) = 0

Solving each factor separately:

2x + 1 = 0, x = -1/2

x - 1 = 0, x = 1

So, the solutions are x = -1/2 and x = 1. However, when we plug in x = 1 into the original equation:

(1) - 1 = 2(1)² - 2
0 = 0

The left side and the right side of the equation are equal, which means x = 1 is not an extraneous solution. Therefore, the extraneous solution is x = -1/2.

Learn more about extraneous solution