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Identities for Irrational Numbers

If x=5+2√6,...

Question

If $x = 5 + 2 \sqrt{6},$ then $\sqrt{\frac{x}{2}} - \frac{1}{\sqrt{2 x}} =$

A

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B

2

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C

3

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D

4

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Solution

The correct option is B 2
(B) Given, x=5+26√

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| 2 x - 1 | + | 2 x - 2 | = 6

x \in

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

, then the value of

(1 - x^{2} + x)^{6} - (1 - x + x^{2})^{6} =

lim x \to - \infty (\sqrt{x^{6} + a x^{5} + b x^{3} - c x + d -} \sqrt{x^{6} - 2 x^{5} + x^{3} + x + 1}) = 2

I = \int \frac{x^{3}}{\sqrt{x^{2} + 2 x + 5}} d x = \frac{1}{6} f (x) - \frac{A}{120} g (x) + C

f (x) = (2 x^{2} - 5 x - 36) \sqrt{x^{2} + 2 x + 5}, g (x) = log (x + 1 + \sqrt{x^{2} + 2 x + 5})

. Then, A is equal to

I = \int \frac{(2 x - 3)^{1 / 2}}{(2 x - 3)^{1 / 3} + 1} d x

= 3 [\frac{1}{7} (2 x - 3)^{7 / 6} - \frac{1}{5} (2 x - 3)^{5 / 6} + \frac{1}{3} (2 x - 3)^{1 / 2} - (2 x - 3)^{1 / 6} + g (x)] + C

then g(x) is equal to

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