Question

Solve. Check for extraneous solutions.
sqrt(x+srt2x)=sqrt2x.
Please show step by step instruction. Thankyou.

Answer 1

$$\sqrt{x+\sqrt{2x}}=\sqrt{2x}$$is that correct?

Answer 2

yeah.

Answer 3

@oldrin.bataku

Answer 4

okay, first thing we want to do is square both sides to get rid of the first radicals:$$\sqrt{x+\sqrt{2x}}=\sqrt{2x}\\\left(\sqrt{x+\sqrt{2x}}\right)^2=\left(\sqrt{2x}\right)^2\\x+\sqrt{2x}=2x\\\sqrt{2x}=2x-x\\\sqrt{2x}=x$$now we square again:$$\left(\sqrt{2x}\right)^2=x^2\\2x=x^2\\x^2-2x=0\\x(x-2)=0$$

Answer 5

to verify these solutions are not extraneous, plug them back in.

Answer 6

How? And thank you