Question

Algebra 2 help:

Solve. Check for extraneous solutions.

(√5-x) - √x = 1

Also, "5-x" is all under a radicand
I have an idea of what to do to solve it, but if someone could walk me through it that would be awesome (final answer is 1 [according to key])

Answer 1

sqrt(5-x) = 1 + sqrt(x)

take square on both sides:

5-x = (1+sqrt(x)) ^2

5 - x = (1+sqrtx)(1+sqrtx)

5 - x = 1 + 2sqrt(x) + x

5 - 2x - 1 = 2sqrt x

(4 - 2x) / 2 = sqrt x

2 - x = sqrt x

Taking square on both sides:

(2-x)^2 = (sqrt x)^2

(2-x)^2 = x

Answer 2

Now solve this and you'll get 2 valuse..

Answer 3

values*