How do you solve #sqrt(x+2)-7=sqrt(x+9#?

1 Answer

Answer:

No solutions exist.

Explanation:

#sqrt(x+2) - 7 = sqrt (x+9) #. Squaring both sides , we get

#(cancelx+2) - 2*7*sqrt(x+2) +49 = (cancelx+9) # or

#2-14 sqrt(x+2)+49 =9 or 14 sqrt(x+2)=42 or sqrt(x+2) =3#

Squaring both sides , we get #x+2 =9 or x=7# [Ans]

Check:

#sqrt(7+2) - 7 = sqrt (7+9) #

#sqrt(9) - 7 = sqrt (16) #

#3 - 7 = 4#

#-4 = 4#

No solutions exist.

I entered the equation into a computation engine named, WolframAlpha ; it returned that no solutions exist.