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# question

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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