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Concept of Inequality

If x=3+8, fin...

Question

If x = 3+ $\sqrt{8}$ , find the value of $x^{2} + \frac{1}{x^{2}}$

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Solution

We know that. We have to find the value of . As therefore,

We know that rationalization factor for is . We will multiply numerator and denominator of the given expression by, to get

Putting the value of x and , we get

Hence the given expression is simplified to.

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x = (3 + \sqrt{8})

, find the value of

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

\frac{1}{x}

= 3, then find the value of

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

x = 3 + \sqrt{8}

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

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

find the values of

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

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

x = 3 - 2 \sqrt{2}

, find the value of:
i)

\frac{1}{x}

x + \frac{1}{x}

x - \frac{1}{x}

\sqrt{x} + \frac{1}{\sqrt{x}}

\sqrt{x} - \frac{1}{\sqrt{x}}

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

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

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