How would you simplify √x+1=3−√x−2?

1 Answer
David B.
Apr 19, 2016

Make a simplifying substitution, like y2=x+1, then solve to find x=3

Explanation:

One way to solve this type of equation is by doing substitutions to simplify one of the square-roots. In this case, it would be really nice if we could do the square root of x+1 on the left hand side, so let's make a substitution that allows that to happen, i.e. let

y2=x+1

From which we can solve for x, so that we can substitute that expression into the rest of the equation:

x=y2−1

Substituting these into the equation we get:

y=3−√y2−3

let's take the 3 to the other side (subtract 3 from both sides) and then square both sides and then simplify:

(y−3)2=y2−3

y2−6y+9=y2−3

−6y−12=0

−6y=−12

y=2

Finally, we can substitute this into our original expression for x in terms of y

x=22−1=3

Let's check this answer by substituting it into the original equation:

√3+1=3−√3−2

2=2 correct!

Related questions
See all questions in Radical Equations
Impact of this question
1813 views around the world
You can reuse this answer
Creative Commons License