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Find all nonnegative numbers x such that sqrt(x) + 2 = sqrt(x+100)

 Sep 5, 2022
 #1
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The solutions are 20 and 40.

 Sep 5, 2022
 #2
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Guest, that is wrong.

 

We have \(\sqrt{x} + 2 = \sqrt{x+100}\). Squaring both sides, we have \(x+4+4\sqrt{x}=x+100\). Combining like terms, we get \(4\sqrt{x}=96\), thus \(\sqrt{x}=24.\) So we have \(\boxed{x=24^2=576.}\) Plugging this in, we see see that it is a solution to the equation. \(\square\)

billy.zhang  Sep 5, 2022

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