How do you solve #sqrt(x + 10) = x - 2#?
The only solution is
See explanation below about arithmetic square root.
First of all, we assume that the equation should be solved for real numbers
When square root is involved and we plan to raise both sides of an equation to the power of 2 to get rid of it, we have to start from the domain where the equation can have sense. In this case, the set of real numbers where the solution should exist is defined as
Another restriction is related to the fact that, when we use a notation
This agreement necessitates that the right side of an equation must be non-negative, that is
Combination of two restrictions,
With this restriction in mind, let's square the equation:
After opening the parenthesis it's transformed into
Two roots of this equation are
Only the first solution satisfy the initial restriction
and the right side is
This is an identity