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Polynomials

If x=2+3, fin...

Question

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

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Solution

Given that, hence $\frac{1}{x}$ is given as

.We are asked to find

We know that rationalization factor for is . We will multiply each side of the given expression by, to get

Therefore,

Hence value of the given expression is.

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Similar questions

Q. Find the value of x,

{tan}^{- 1} x + 2 {cot}^{- 1} x = \frac{2 π}{3}

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}}

t a n^{- 1} \frac{x - 3}{x - 4} + t a n^{- 1} \frac{x + 3}{x + 4} = \frac{3}{4}

, then find the value of

x

{tan}^{- 1} \frac{x - 3}{x - 4} + {tan}^{- 1} \frac{x + 3}{x + 4} = \frac{π}{4}

, then find the value of

x

{tan}^{- 1} (\frac{x - 1}{x - 2}) + {tan}^{- 1} (\frac{x + 1}{x + 2}) = \frac{π}{4}

, find the value of

x

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