If x-1-3-1 then the value of x-1-x is-2 Marks-

X=1/√(3)+1×√(3) 1/√(3) 1=√(3) 1/2 [1 Mark] x+1/x=√(3) 1/2+2/(√(3) 1) =(√(3) 1)^2+4/2(√(3) 1) nbsp; nbsp; =3+1 2√(3)+4/2(√(3) 1) =8 2 √(3)/2(√(3) 1) n ...

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Byju's Answer

Standard IX

Mathematics

Rationalising Factor

If x=1/√3+1 t...

Question

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

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Solution

$x = \frac{1}{\sqrt{3} + 1} \times \frac{\sqrt{3} - 1}{\sqrt{3} - 1} = \frac{\sqrt{3} - 1}{2} [1 M a r k] x + \frac{1}{x} = \frac{\sqrt{3} - 1}{2} + \frac{2}{(\sqrt{3} - 1)} = \frac{(\sqrt{3} - 1)^{2} + 4}{2 (\sqrt{3} - 1)} = \frac{3 + 1 - 2 \sqrt{3} + 4}{2 (\sqrt{3} - 1)} = \frac{8 - 2 \sqrt{3}}{2 (\sqrt{3} - 1)}$
[1 Mark]

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If x=1√3+1 then the value of x+1x is [2 Marks]

x=1√3+1×√3−1√3−1=√3−12[1Mark]x+1x=√3−12+2(√3−1)=(√3−1)2+42(√3−1)=3+1−2√3+42(√3−1)=8−2√32(√3−1) [1 Mark]

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