BigBeachBanana
Senior Member
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- Nov 19, 2021
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[math]\large \sqrt{x-\frac{1}{x}} + \sqrt{1-\frac{1}{x}}=x[/math]Solve for [imath]\large x.[/imath]
Just wondering ... Is one of the minus signs meant to be a plus?[math]\large \sqrt{x-\frac{1}{x}} + \sqrt{1-\frac{1}{x}}=x[/math]Solve for [imath]\large x.[/imath]
I tripled-checked before I post...considering the number of mistakes I've been making. The OP is correct. It is a tougher one but can be solved algebraically. Here are some hints.Just wondering ... Is one of the minus signs meant to be a plus?
FYI: the problem got me for 2 days already.
I actually had done exactly what you did but I failed to let t= \(\displaystyle \sqrt{x^3-x^2-x+1}\)[math]\sqrt{\frac{x^2-1}{x}}+\sqrt{\frac{x-1}{x}}=x\Leftrightarrow \sqrt{x^2-1}+\sqrt{x-1}=x\sqrt{x}\Leftrightarrow\\ \Leftrightarrow x^2+x-2+2\sqrt{x^3-x^2-x+1}=x^3\Leftrightarrow 2\sqrt{x^3-x^2-x+1}=\left(x^3-x^2-x+1\right)+1[/math]
Why would you do this to us mortals?? Some people, like red12dog34, have the ability to just write down the solution with ease but others.....FYI: the problem got me for 2 days already.