Emily778 one year ago Solve. Check for extraneous solutions. sqrt(x+srt2x)=sqrt2x. Please show step by step instruction. Thankyou.

1. oldrin.bataku

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

2. Emily778

yeah.

3. Emily778

@oldrin.bataku

4. oldrin.bataku

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:$$\left(\sqrt{2x}\right)^2=x^2\\2x=x^2\\x^2-2x=0\\x(x-2)=0$$

5. oldrin.bataku

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

6. Emily778

How? And thank you