How do you simplify $sqrt(2x+2) - sqrt(x+2) = 1$ ?

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Answer 1 · 2016-07-06T15:43:29

$x = 7$

Squaring both sides

$2x+2-2sqrt((2x+2)(x+2))+x+2=1$

grouping

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

squaring both sides again

$9(x^2+2x+1)=4(2x+2)(x+2)$

or

$(x+1)(x-7)=0$

Testing the roots in

$sqrt(2x+2) - sqrt(x+2) = 1$

we choose $x = 7$

How do you simplify sqrt(2x+2) - sqrt(x+2) = 1sqrt(2x+2) - sqrt(x+2) = 1?