MHB Real Solutions for x in a Complex Equation

[mathdad]

Find all real solutions of the equation.

x - sqrt {x^2 - x} = sqrt {x}, where x > 0.

Since x cannot be 0, I divided through by sqrt {x} to simplify the equation.

I did a lot of math on paper and ended up with x = 1 as the answer.

I decided to substitute x = 1 into the original equation.

1 - sqrt {1^2 - 1} = sqrt {1}

1 - sqrt {1 - 1} = 1

1 - sqrt {0} = 1

1 - 0 = 1

1 = 1

What do you say?

 

[topsquark]

Find all real solutions of the equation.

x - sqrt {x^2 - x} = sqrt {x}, where x > 0.

Since x cannot be 0, I divided through by sqrt {x} to simplify the equation.

I did a lot of math on paper and ended up with x = 1 as the answer.

I decided to substitute x = 1 into the original equation.

1 - sqrt {1^2 - 1} = sqrt {1}

1 - sqrt {1 - 1} = 1

1 - sqrt {0} = 1

1 - 0 = 1

1 = 1

What do you say?

Looks good.

-Dan

 

[mathdad]

Good to know that I am right.