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!