If x -1-3-1 then the value of x -1- x isA- 8-2 -3-2 -3-1B- -3-12C- 1-5D- -2-3

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

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

Byju's Answer

Standard IX

Mathematics

Rationalisation

If x =1/√3+1 ...

Question

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

$\frac{8 - 2 \sqrt{3}}{2 \sqrt{3} - 1}$

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

$\frac{\sqrt{3}}{2}$

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

$\frac{1}{5}$

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

$\frac{\sqrt{2}}{3}$

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

Open in App

Solution

The correct option is A
$\frac{8 - 2 \sqrt{3}}{2 \sqrt{3} - 1}$

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

Suggest Corrections

Similar questions

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

Q. The lines

\frac{x + 3}{- 3} = \frac{y - 1}{1} = \frac{z - 5}{5}

and

\frac{x + 1}{- 1} = \frac{y - 2}{α} = \frac{z - 5}{5}

are coplanar. Then the value of

α

Q. If

α

and

β

are the roots of the quadratic equation

(x - 2) (x - 3) + (x - 3) (x + 1) + (x + 1) (x - 2) = 0

, then the value of

\frac{1}{(α + 1) (β + 1)} + \frac{1}{(α - 2) (β - 2)} + \frac{1}{(α - 3) (β - 3)}

Join BYJU'S Learning Program

If x=1√3+1 then the value of x+1x is

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

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