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Expansion of (x+a)(x+b)

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

Question

If $x + \frac{1}{x} = 5$ , find the value of $x^{3} + \frac{1}{x^{3}}$

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Solution

In the given problem, we have to find the value of

Given

We shall use the identity

Here putting,

Hence the value of is

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x - \frac{1}{x} = 5

, find the value of

x^{3} - \frac{1}{x^{3}}

x - \frac{1}{x} = 7

, find the value of

x^{3} - \frac{1}{x^{3}}

Find the value of

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

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

x - \frac{1}{x} = 3 + 2 \sqrt{2}

, find the value of

x^{3} - \frac{1}{x^{3}}

x = 9 - 4 \sqrt{5}

then , find the value of

x^{3} - \frac{1}{x^{3}}

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