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Emily778

  • one year ago

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

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  1. oldrin.bataku
    • one year ago
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    $$\sqrt{x+\sqrt{2x}}=\sqrt{2x}$$is that correct?

  2. Emily778
    • one year ago
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    yeah.

  3. Emily778
    • one year ago
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    @oldrin.bataku

  4. oldrin.bataku
    • one year ago
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    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
    • one year ago
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    to verify these solutions are not extraneous, plug them back in.

  6. Emily778
    • one year ago
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    How? And thank you

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