Question

Israel started to solve a radical equation in this way:

Answer 1

I think the correct answer from the choices listed above is option D. The mistake that he did was that he did not check extraneous solutions.

√(-2 + 6 ) - 4 = - 2
√2  - 4 = -2
- 2 = - 2
and: √(- 5 + 6 ) - 4 = - 5
√ 1 - 4 = - 5
- 3 ≠ - 5

Therefore, x = - 5  does not work.

Answer 2

Only x = - 2 works in the original equation. 
√(-2 + 6 ) - 4 = - 2
√2  - 4 = -2
- 2 = - 2
and: √(- 5 + 6 ) - 4 = - 5
√ 1 - 4 = - 5
- 3 ≠ - 5 ( x = - 5  does not work ).
Answer: D ) He did not check for extraneous solutions.