Question

Li Juan solves the equation below by first squaring both sides of the equation.
`√(3-2w)=w+6`

What extraneous solution does Li Juan obtain?

Answer 1

w = -11

Explanation:

`√(3 - 2w) = w + 6`

`(√(3 - 2w))^2 = (w + 6)^2`

`3 - 2w = w^2 + 12w + 36`

`w^2 + 14w + 33 = 0`

`(w + 11)(w + 3) = 0`

`w + 11 = 0` or
`w + 3 = 0`

`w = -11` or
`w = -3`

When you square both sides of an equation, you must check all solutions for extraneous solutions.

Check w = -11.

`√(3 - 2w) = w + 6`

`√(3 - 2(-11)) = -11 + 6`

`√(3 + 22) = -5`

`√(25) = -5`

`5 = -5`

This is a false statement, so the solution w = -11 is extraneous since it does not satisfy the original equation.

Check w = -3.

`√(3 - 2w) = w + 6`

`√(3 - 2(-3)) = -3 + 6`

`√(3 + 6) = 3`

`√(9) = 3`

`3 = 3`

This is a true statement, so the solution w = -3 is valid.

Answer: w = -11