MHB Solving Equation: x = sqrt(3x + x^2 - 3sqrt(3x + x^2))

[mathdad]

Find all real solutions of the equation.

$x = \sqrt{3x + x^2 - 3\sqrt{3x + x^2}}$

Must I square each side twice to start?

$(x)^2 = [\sqrt{3x + x^2 - 3\sqrt{3x + x^2}}]^2$

$x^2 = 3x + x^2 - 3\sqrt{3x + x^2}$

$x^2 - x^2 - 3x = -3\sqrt{3x + x^2}$

$-3x = -3\sqrt{3x + x^2}$

$x = \sqrt{3x + x^2}$

$(x)^2 = [\sqrt{3x + x^2}]^2$

$x^2 = 3x + x^2$

$x^2 - x^2 = 3x$

$0 = 3x$

$0/3 = x$

$0 = x$

Is this right?

 

[Euge]

Yes, it's correct.

 

[mathdad]

Good to know that I am right.