Question

x²+1/x²=2 then x+1/x=?

Answer 1

Two ways  we can do this.

$(x+\frac{1}{x})^2-2*x*\frac{1}{x}=2\\\\(x+\frac{1}{x})^2=4\\\\x+\frac{1}{x}=+2\ or\ -2$

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$x^2+\frac{1}{x^2}=2\\\\x^4+1-2x^2=0\\\\x^2=\frac{+2+-\sqrt{4-4}}{2}=1\\\\x=+1\ or\ -1\\\\Hence\ x+\frac{1}{x}=2\ or\ -2$