What is the value of x^2 + 1/x^2 + 1 using identities

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Solution

$x^{2} + \frac{1}{x^{2}} + 1 = x^{2} + \frac{1}{x^{2}} + 2 - 1 = [x^{2} + \frac{1}{x^{2}} + 2] - {(1)}^{2} = [{(x)}^{2} + {(\frac{1}{x})}^{2} + 2 \times x \times \frac{1}{x}] - {(1)}^{2} = {(x + \frac{1}{x})}^{2} - {(1)}^{2} = (x + \frac{1}{x} + 1) (x + \frac{1}{x} - 1)$

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