Question 870032
I don't this can have a solution, but let's see.
:
{{{sqrt(2x+3) + sqrt(x-2) = 2}}}
subtrac sqrt(x-2) from both sides
{{{sqrt(2x+3) = 2 - sqrt(x-2)}}}
Square both sides, the right side needs to be FOILed
{{{(2x+3) = 4 - 4sqrt(x-2)+ (x-2)}}}
{{{(2x+3) = x + 4 - 2 - 4sqrt(x-2))}}}
{{{(2x+3) = x + 2 - 4sqrt(x-2)}}}
combine like terms on the left
{{{2x - x + 3 - 2 = -4sqrt(x-2)}}}
{{{(x + 1) = -4sqrt(x-2)}}}
square both sides again, the left side is FOILed
{{{x^2 + 2x + 1 = 16(x-2)}}}
{{{x^2 + 2x + 1 = 16x - 32}}}
x^2 + 2x - 16x + 1 + 32 = 0
x^2 - 14x + 33 = 0
Factors to
(x-11)(x-3) = 0
Two solutions
x = 11
x = 3
Try both solutions in the original problem, neither works, so there is no solution