How do you solve: $sqrt(2x+5) - sqrt(x-2) = 3$ ?

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Answer 1 · 2015-04-25T00:16:51

$sqrt(2x+5) - sqrt(x-2)=3$

First isolate one of the square roots:
$sqrt(2x+5)=3+sqrt(x-2)$
Then square each side:
$(sqrt(2x+5))^2=(3+sqrt(x-2))(3+sqrt(x-2))$
$2x+5=9+6sqrt(x-2)+(x-2)$
Simplify the equations leaving the square root on one sided:
$x-2=6sqrt(x-2)$
Square each side:
$(x-2)(x-2)=36(x-2)$
Divide each side by (x-2):
$x-2=36$
so $x=38$

All ways check you answer in the original problem:
$sqrt(2x+5) - sqrt(x-2)=3$
$sqrt(2(38)+5) - sqrt(38-2)=3$
$sqrt(81) - sqrt(36)=3$
$9-6=3$
$3=3$

How do you solve: sqrt(2x+5) - sqrt(x-2) = 3sqrt(2x+5) - sqrt(x-2) = 3?