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

The correct option is B 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 IX

Mathematics

Simplest Form of a Surd

If x=1/√3+1 t...

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 A

$x = \frac{1}{\sqrt{3} + 1} \times \frac{\sqrt{3} - 1}{\sqrt{3} - 1} = \frac{\sqrt{3} - 1}{2} x + \frac{1}{x} = \frac{\sqrt{3} - 1}{2} + \frac{2}{(\sqrt{3} - 1)} = \frac{(\sqrt{3} - 1)^{2} + 4}{2 (\sqrt{3} - 1)} = \frac{3 + 1 - 2 \sqrt{3} + 4}{2 (\sqrt{3} - 1)} = \frac{8 - 2 \sqrt{3}}{2 (\sqrt{3} - 1)}$

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