$\sqrt{x^{2} + 5} = x + 1 ?$ $sqrt( x^2 + 5) = x + 1?$ solve the equation

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Answer 1 · 2017-04-13T19:45:13

$x = 2$ $x=2$

$\sqrt{x^{2} + 5} = x + 1$ $sqrt(x^2+5)=x+1$

$x^{2} + 5 = {(x + 1)}^{2} = x^{2} + 2 x + 1$ $x^2+5=(x+1)^2=x^2+2x+1$

$x^{2} + 5 = x^{2} + 2 x + 1$ $x^2+5=x^2+2x+1$

$2 x - 4 = 0$ $2x-4=0$

$x = 2$ $x=2$

Verify solution using original equation

$\sqrt{2^{2} + 5} = 3$ $sqrt(2^2+5)=3$

$2 + 1 = 3$ $2+1=3$

$x = 2$ $x=2$ is a valid solution

√x2+5=x+1?sqrt( x^2 + 5) = x + 1? solve the equation