# How do you solve #sqrt( x^2+7)=x+1#?

##### 1 Answer

May 8, 2016

#### Explanation:

First square both sides, noting that squaring may introduce spurious solutions...

#x^2+7 = (x+1)^2 = x^2+2x+1#

Subtract

#7 = 2x+1#

Subtract

#6 = 2x#

Divide both sides by

#x = 3#

Check that this is a solution of the original equation:

#sqrt(x^2+7) = sqrt(3^2+7) = sqrt(9+7) = sqrt(16) = 4 = 3+1 = x+1#