Question

Solve √x+7-1=x slove for x

and is it an extraneous solution show work
a) x=3, extraneous
b) x=4, extraneous
c) x=9, not extraneous
d)x=10, not extraneous

Answer 1

The solution to the square root equation √x + 7 - 1 = x is x = 2, which is found by isolating the square root, squaring both sides, and then factoring the resulting quadratic equation. The solution is not extraneous as it satisfies the original equation.

Step-by-step explanation:

To solve the equation, √x + 7 - 1 = x, we first isolate the square root term and then square both sides of the equation to eliminate the square root.

1. Add 1 to both sides: √x + 7 = x + 1.
2. Square both sides: (√x + 7)2 = (x + 1)2.
3. Expand both sides: x + 7 = x2 + 2x + 1.
4. Rearrange into standard quadratic form: x2 + x - 6 = 0.
5. Factor the quadratic: (x + 3)(x - 2) = 0.
6. Solve for x: x = -3 (extraneous, as it would result in a negative under the square root) or x = 2.
7. Check the solution: √(2 + 7) - 1 = √9 - 1 = 3 - 1 = 2, which matches the original x value, so it is not extraneous.

Thus, the solution is x = 2, and it is not an extraneous solution since it satisfies the original equation when plugged back in.