Question

How to solve: \(\sqrt{x - 2} - \sqrt{x + 10} = 2\)? (The answer is that there are no solutions, however, I can't seem to work it out...)

Answer 1

Are you familiar with logarithmic functions?

Answer 2

No, I am not.

Answer 3

u first need to square everything

Answer 4

2 mins plz

Answer 5

maybe one way is to do this:
\[ \sqrt{x - 2} - \sqrt{x + 10} = 2 \\
\sqrt{x - 2} = 2+\sqrt{x + 10} \]
now square both sides to get
\[ x-2 = 4+x+10 +4 \sqrt{x+10} \]
after we simplify we get
\[ - 4= \sqrt{x+10} \]
and (because we only use the "principal square root" i.e. the positive root)
there is no solution.

Answer 6

Thank you very much!