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Expansion of (x^2 - y^2)

If x+1 x=5, f...

Question

If $x + \frac{1}{x} = \sqrt{5}$ , find the value of $x^{2} + \frac{1}{x^{2}}$ and $x^{4} + \frac{1}{x^{4}}$ .

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Solution

In the given problem, we have to find and

We have

On squaring both sides we get,

We shall use the identity

Again squaring on both sides we get,

We shall use the identity

Hence the value ofis and is .

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Similar questions

x - \frac{1}{x} = 3,

find the values of

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

x^{4} + \frac{1}{x^{4}} .

x^{4} + \frac{1}{x^{4}} = 194,

x^{3} + \frac{1}{x^{3}}, x^{2} + \frac{1}{x^{2}}

x + \frac{1}{x}

If $x + \frac{1}{x} = 3$ , calculate $x^{2} + \frac{1}{x^{2}}, x^{3} + \frac{1}{x^{3}}$ and $x^{4} + \frac{1}{x^{4}}$

x^{2} + \frac{1}{x^{2}} = 18,

find the values of

x + \frac{1}{x} and x - \frac{1}{x} .

(x + \frac{1}{x}) = 4

, find the values of
(i)

(x^{2} + \frac{1}{x^{2}})

(x^{4} + \frac{1}{x^{4}})

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