Using the identity, (a+b)^2 nbsp;= a^2 nbsp;+ b^2 nbsp;+2ab we get, nbsp;(x+1/x)^2 = x^2 + (1/x)^2 + 2 × x ×1/x =x^2 + 1/x^2 + 2 ...

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Expansion of (a ± b)³

Expand: x+1/x...

Question

$Expand: (x + \frac{1}{x})^{2}$

$x^{2} - \frac{1}{x^{2}} + 2$

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$x^{2} + \frac{1}{x^{2}} - 2$

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$x^{2} + \frac{1}{x^{2}} + 2$

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$x^{2} + \frac{1}{x} + 2$

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Solution

The correct option is C
$x^{2} + \frac{1}{x^{2}} + 2$

Using the identity,
$(a + b)^{2} = a^{2} + b^{2} + 2 a b$

we get,

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

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