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

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Answer 1 · 2016-08-11T18:44:10

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

There are no Extraneous Solns.

We rewrite the given eqn. as, #sqrt(x+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.