MHB Find All Real Solutions: Is x = 0 a solution to the equation?

[mathdad]

Find all the real solutions of the equation.

Let rt = root

x = rt{3x + x^2 - 3•rt{3x + x^2}}

(x)^2 = [rt{3x + x^2 - 3•rt{3x + x^2}}]^2

x^2 = 3x + x^2 - 3•rt{3x + x^2}

x^2 - x^2 - 3x = - 3•rt{3x + x^2}

-3x = -3•rt{3x + x^2}

-3x/-3 = rt{3x + x^2}

x = rt{3x + x^2}

(x)^2 = [rt{3x + x^2}]^2

x^2 = 3x + x^2

x^2 - x^2 = 3x

0 = 3x

0/3 = x

0 = x

Correct?

 

[Prove It]

Find all the real solutions of the equation.

Let rt = root

x = rt{3x + x^2 - 3•rt{3x + x^2}}

(x)^2 = [rt{3x + x^2 - 3•rt{3x + x^2}}]^2

x^2 = 3x + x^2 - 3•rt{3x + x^2}

x^2 - x^2 - 3x = - 3•rt{3x + x^2}

-3x = -3•rt{3x + x^2}

-3x/-3 = rt{3x + x^2}

x = rt{3x + x^2}

(x)^2 = [rt{3x + x^2}]^2

x^2 = 3x + x^2

x^2 - x^2 = 3x

0 = 3x

0/3 = x

0 = x

Correct?

Your method is correct. You must also check that the answer you have found actually works to make the equation true.

 

[mathdad]

Check:

Let x = 00 = rt{3(0) + (0)^2 - 3•rt{3(0) + (0)^2}}

0 = rt{0 + 0 - 3rt{0 + 0}}

0 = rt{0 + 0 - 3rt{0}}

0 = rt{0 + 0 - 0}

0 = rt{0}

0 = 0

It checks to be true.