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

The correct option is D 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) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Addition of Rational Expressions

If x=1/√3+1 t...

Question

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A

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

Suggest Corrections

If x=1√3+1 then the value of x+1x is

The correct option is A x=1√3+1×√3−1√3−1=√3−12x+1x=√3−12+2(√3−1)=(√3−1)2+42(√3−1)=3+1−2√3+42(√3−1)=8−2√32(√3−1)

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