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#