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

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Answer 1 · 2016-05-08T12:22:59

$x=3$

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

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

Subtract $x^2$ from both ends to get:

$7 = 2x+1$

Subtract $1$ from both sides to get:

$6 = 2x$

Divide both sides by $2$ and transpose to get:

$x = 3$

Check that this is a solution of the original equation:

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

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