How do you solve $sqrt(2x+3)-sqrt( x+1) =1$ ?

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Answer 1 · 2018-04-29T19:26:16

The two solutions are $x=3$ and $x=-1$ .

Isolate one of the radicals, square both sides, isolate the other radical, then square both sides again:

$sqrt(2x+3)-sqrt(x+1)=1$

$sqrt(2x+3)=1+sqrt(x+1)$

$(sqrt(2x+3))^2=(1+sqrt(x+1))^2$

$2x+3=1+2sqrt(x+1)+x+1$

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

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

$(x+1)^2/2^2=(sqrt(x+1))^2$

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

$x^2+2x+1=4x+4$

$x^2-2x-3=0$

$(x-3)(x+1)=0$

$x=3,-1$

Those are the solutions to the problem. Hope this helped!

How do you solve sqrt(2x+3)-sqrt( x+1) =1sqrt(2x+3)-sqrt( x+1) =1?