How do you solve sqrt(x+6)-5=x+1x+65=x+1 and find any extraneous solutions?

1 Answer
Aug 11, 2016

The Son. Set ={-6,-5}={6,5}.

There are no Extraneous Solns.

Explanation:

We rewrite the given eqn. as, sqrt(x+6)=5+x+1=x+6x+6=5+x+1=x+6

:. (sqrt(x+6))^2=(x+6)^2

:. (x+6)-(x+6)^2=0

:. (x+6)(1-x-6)=0.

:. -(x+6)(x+5)=0

:. x=-6, or, x=-5

these roots satisfy the given eqn.

Hence, The Son. Set ={-6,-5}.

There are no Extraneous Solns.