Please help me with solving sqrt(4 - sqrt(x)) = 1 - sqrt(3)
S Samuel New member Joined Sep 11, 2006 Messages 2 Sep 11, 2006 #1 Please help me with solving sqrt(4 - sqrt(x)) = 1 - sqrt(3)
D Denis Senior Member Joined Feb 17, 2004 Messages 1,707 Sep 12, 2006 #2 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
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
S Samuel New member Joined Sep 11, 2006 Messages 2 Sep 12, 2006 #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?
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?
S soroban Elite Member Joined Jan 28, 2005 Messages 5,586 Sep 12, 2006 #4 Hello, Samuel! You have a valid concern . . . \(\displaystyle \L\sqrt{4\,-\,\sqrt{x}} \:= \:1\,-\,\sqrt{3}\) Click to expand... Square both sides: \(\displaystyle \L\,4\,-\,\sqrt{x} \:=\:1\,-\,2\sqrt{3}\,+\,3\;\;\Rightarrow\;\;\sqrt{x}\:=\:2\sqrt{3}\) Therefore: \(\displaystyle \L\:x\,=\,12\) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Check: \displaystyle \:Does 4 − 12⏟ = 1 − 3⏟\displaystyle \,\underbrace{\sqrt{4\,-\,\sqrt{12}}}\:=\:\underbrace{1\,-\,\sqrt{3}}4−12=1−3 ? . . . . . . . . . . . . . ↓\displaystyle \downarrow↓ . . . . . . .↓\displaystyle \downarrow↓ No . . . . . 0.73205080 . .-0.732050808 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ You "eyeballed" the problem and saw that it had no solution. Good work!
Hello, Samuel! You have a valid concern . . . \(\displaystyle \L\sqrt{4\,-\,\sqrt{x}} \:= \:1\,-\,\sqrt{3}\) Click to expand... Square both sides: \(\displaystyle \L\,4\,-\,\sqrt{x} \:=\:1\,-\,2\sqrt{3}\,+\,3\;\;\Rightarrow\;\;\sqrt{x}\:=\:2\sqrt{3}\) Therefore: \(\displaystyle \L\:x\,=\,12\) ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ Check: \displaystyle \:Does 4 − 12⏟ = 1 − 3⏟\displaystyle \,\underbrace{\sqrt{4\,-\,\sqrt{12}}}\:=\:\underbrace{1\,-\,\sqrt{3}}4−12=1−3 ? . . . . . . . . . . . . . ↓\displaystyle \downarrow↓ . . . . . . .↓\displaystyle \downarrow↓ No . . . . . 0.73205080 . .-0.732050808 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ You "eyeballed" the problem and saw that it had no solution. Good work!