Question

Solve for X. Check for extraneous answers.
sqrt{x + sqrt{2x}}=2

Answer 1

\[\sqrt{x + \sqrt{2x}}=2 \]

Answer 2

square roots are pesky. The first thing to do is square both sides to get rid of one of them. Then rearrange and square again until you have no square roots. What do you get thus far?

Answer 3

\[\sqrt{x + \sqrt{2x}}=2 \]
\[x+ \sqrt{2x} =4\]
\[\sqrt{2x}= -x+4 \]
\[2x =x^2 +16\]
What do I do?

Answer 4

Almost
\[ \sqrt{2x} = -x + 4 \ \ \Rightarrow \ \ 2x = x^2 - 8x + 64 \]
Now solve the quadratic

Answer 5

correction: 2x = x^2 -8x + 16

Hence

x^2 - 10x + 16 = 0

Answer 6

You will find two solutions. Double check whether each of them satisfies the original equation.

Answer 7

Extraneous answer: x=8
Solution: X=2
Thank you!

Answer 8

Right