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

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oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.1$$\sqrt{x+\sqrt{2x}}=\sqrt{2x}$$is that correct?

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.1okay, first thing we want to do is square both sides to get rid of the first radicals:$$\sqrt{x+\sqrt{2x}}=\sqrt{2x}\\\left(\sqrt{x+\sqrt{2x}}\right)^2=\left(\sqrt{2x}\right)^2\\x+\sqrt{2x}=2x\\\sqrt{2x}=2xx\\\sqrt{2x}=x$$now we square again:$$\left(\sqrt{2x}\right)^2=x^2\\2x=x^2\\x^22x=0\\x(x2)=0$$

oldrin.bataku
 2 years ago
Best ResponseYou've already chosen the best response.1to verify these solutions are not extraneous, plug them back in.
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