If x -1-3-1 then the value of x -1- x isA- 8-2 -3-2 -3-1B- None of these D- 12-5

The correct option is A x=1/√(3)+1×√(3) 1/√(3) 1=√(3) 1/2 x+1/x=√(3) 1/2+2/(√(3) 1) =(√(3) 1)^2+4/2(√(3) 1) =3+1 2√(3)+4/2(√(3) 1) =8 2 √(3)/2(√(3) 1) ...

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Byju's Answer

Standard X

Mathematics

Addition of Rational Expressions

If x =1/√3+1 ...

Question

If $x = \frac{1}{\sqrt{3} + 1}$ then the value of $x + \frac{1}{x}$ is

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Solution

The correct option is
option B. None of these
$x = \frac{1}{\sqrt{3} + 1} \times \frac{\sqrt{3} - 1}{\sqrt{3} - 1} = \frac{\sqrt{3} - 1}{2} x + \frac{1}{x} = \frac{\sqrt{3} - 1}{2} + \frac{2}{(\sqrt{3} - 1)} = \frac{(\sqrt{3} - 1)^{2} + 4}{2 (\sqrt{3} - 1)} = \frac{3 + 1 - 2 \sqrt{3} + 4}{2 (\sqrt{3} - 1)} = \frac{8 - 2 \sqrt{3}}{2 (\sqrt{3} - 1)}$
So, $x + \frac{1}{x} = \frac{8 - 2 \sqrt{3}}{2 \sqrt{3} - 2}$
Hence, The correct option is option B.

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