Find the square of x+1 x -1 - Vidyadip

Question

Find the square of $x+\frac{1}{x}-1$

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Answer

$ \left(\mathrm{x}+\frac{1}{\mathrm{x}}-1\right)^2$
$=(\mathrm{x})^2+\left(\frac{1}{\mathrm{x}}\right)^2+(-1)^2+2 \times \mathrm{x} \times \frac{1}{\mathrm{x}}+2 \times \frac{1}{\mathrm{x}} \times(-1)+2(-1) \times \mathrm{x}$
$ =\mathrm{x}^2+\frac{1}{\mathrm{x}^2}+1+2-\frac{2}{\mathrm{x}}-2 \mathrm{x}$
$ =\mathrm{x}^2+\frac{1}{\mathrm{x}^2}+3-\frac{2}{\mathrm{x}}-2 \mathrm{x}$

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