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Emily778
Group Title
Solve. Check for extraneous solutions.
sqrt(x+srt2x)=sqrt2x.
Please show step by step instruction. Thankyou.
 11 months ago
 11 months ago
Emily778 Group Title
Solve. Check for extraneous solutions. sqrt(x+srt2x)=sqrt2x. Please show step by step instruction. Thankyou.
 11 months ago
 11 months ago

This Question is Closed

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

Emily778 Group TitleBest ResponseYou've already chosen the best response.0
@oldrin.bataku
 11 months ago

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

oldrin.bataku Group TitleBest ResponseYou've already chosen the best response.1
to verify these solutions are not extraneous, plug them back in.
 11 months ago

Emily778 Group TitleBest ResponseYou've already chosen the best response.0
How? And thank you
 11 months ago
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