What is expansion of x -1- x 2 -B- x2-1-x2-2C- x2-1-x2-2D- None of the above

The correct option is A x^2 + 1/x^2 + 2We have the identity: (a+b)^2 = a^2 + b^2 +2ab ∴ (x+1/x)^2 = x^2 + (1/x)^2 + 2 × x ×1/x =x^2 + 1/x^2 + 2 ...

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Standard IX

Mathematics

Algebraic Identities

What is expan...

Question

What is expansion of $(x + \frac{1}{x})^{2}$ ?

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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None of the above

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Solution

The correct option is C $x^{2} + \frac{1}{x^{2}} + 2$
We have the identity:

$(a + b)^{2} = a^{2} + b^{2} + 2 a b$

$∴ (x + \frac{1}{x})^{2}$

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

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

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What is expansion of (x+1x)2?

The correct option is C x2+1x2+2We have the identity: (a+b)2=a2+b2+2ab ∴(x+1x)2 =x2+(1x)2+2×x×1x =x2+1x2+2

What is expansion of $(x + \frac{1}{x})^{2}$ ?

The correct option is C $x^{2} + \frac{1}{x^{2}} + 2$
We have the identity:

$(a + b)^{2} = a^{2} + b^{2} + 2 a b$

$∴ (x + \frac{1}{x})^{2}$

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

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