How do you solve #sqrt(x+5) + sqrt(x+15) = sqrt(9x+40)#?
Square, rearrange and square again to get a quadratic, one of whose roots is a valid solution:
Note that both sides are non-negative, being the sums of non-negative square roots. So squaring both sides will not introduce spurious solutions.
So square both sides to get:
Note that a valid solution will require
Square both sides (which may introduce extraneous solutions with
Subtract the right hand side from the left to get:
Divide through by
Solve using the quadratic formula: