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

1 Answer
Alan P.
Aug 31, 2016

color(green)(x=13/4 = 3 1/4)

Explanation:

Given
color(white)("XXX")sqrt(x+3)-sqrt(x-1)=1

color(white)("XXX")rarr sqrt(x+3)=1+sqrt(x-1)

Squaring both sides:
color(white)("XXX")cancel(x)+3=cancel(1)+2sqrt(x-1)+cancel(x)cancel(-1)

color(white)("XXX")rarr 2sqrt(x-1)=3

color(white)("XXX")rarr sqrt(x-1)=3/2

Squaring both sides again
color(white)("XXX")rarr x-1=9/4

color(white)("XXX")rarr x=13/4

Related questions
See all questions in Radical Equations
Impact of this question
1424 views around the world
You can reuse this answer
Creative Commons License