need help solving sqrt(4-sqrt(x)) = 1-sqrt(3)

What is it you don't understand, Sammy me boy?

sqrt(4-sqrt(x)) = 1-sqrt(3)

Start by squaring both sides:
4 - sqrt(x) = 1 - 2sqrt(3) + 3
 
thank you. but what threw me off is wouldn't there have to be an imaginary number answer since the right side is negative and the left positive?
 
Hello, Samuel!

You have a valid concern . . .


\(\displaystyle \L\sqrt{4\,-\,\sqrt{x}} \:= \:1\,-\,\sqrt{3}\)

Square both sides: \(\displaystyle \L\,4\,-\,\sqrt{x} \:=\:1\,-\,2\sqrt{3}\,+\,3\;\;\Rightarrow\;\;\sqrt{x}\:=\:2\sqrt{3}\)

Therefore: \(\displaystyle \L\:x\,=\,12\)

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Check: \displaystyle \:Does 412=13\displaystyle \,\underbrace{\sqrt{4\,-\,\sqrt{12}}}\:=\:\underbrace{1\,-\,\sqrt{3}} ?
. . . . . . . . . . . . . \displaystyle \downarrow . . . . . . .\displaystyle \downarrow
No . . . . . 0.73205080 . .-0.732050808

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You "eyeballed" the problem and saw that it had no solution.

Good work!

 
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