√2x + 1 = 1 + √x --Major problems. Please help?

Question

I could go through the entire list of the different ways I've approached this and three similar equations, but that would take far too long. What matter is that I have no clue how to come up with '0,4', which is the answer in the text.

Despite laying out a formula to solve this problem, I can't seem figure out how to utilize the method properly. I suspect that the teacher who wrote the workbook from which I'm working omitted a step or two.

Answer 1

Careful when you type the question.

It should be

√(2x + 1) = 1 + √x

Anyhow, start by squaring boths sides:

(which cancels out the root on the left side)

(2x + 1) = 1 + 2√(x)  + x

The 1's cancle out, and the x's can be grouped:

x - 2√(x) = 0

Let √(x) = y

y^2 - 2y = 0

You can now use the quadratic equation, or just factor the expression:

y ( y-2) = 0

so y = 0 or 2

and x = 0 or 4 (since √(x) = y, or x = y^2)