How do you solve sqrt( x^2+7)=x+1x2+7=x+1?

1 Answer
May 8, 2016

x=3x=3

Explanation:

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

x^2+7 = (x+1)^2 = x^2+2x+1x2+7=(x+1)2=x2+2x+1

Subtract x^2x2 from both ends to get:

7 = 2x+17=2x+1

Subtract 11 from both sides to get:

6 = 2x6=2x

Divide both sides by 22 and transpose to get:

x = 3x=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+1x2+7=32+7=9+7=16=4=3+1=x+1