Question
If $\text{x}=2+\sqrt{3}$ then $\Big(\text{x}+\frac{1}{\text{x}}\Big)$ equals :
✓
Answer
- 4
Solution :
$\text{x}=2+\sqrt{3}$
$\therefore\frac{1}{\text{x}}=\frac{1}{2+\sqrt{3}}$
$=\frac{1}{2+\sqrt{3}}\times\frac{2-\sqrt{3}}{2-\sqrt{3}}$
$=\frac{2-\sqrt{3}}{2^2-\big(\sqrt{3}\big)^2}$
$=\frac{2-\sqrt{3}}{4-3}$
$=2-\sqrt{3}$
$\therefore\Big(\text{x}+\frac{1}{\text{x}}\Big)=\big(2+\sqrt{3}\big)+\big(2-\sqrt{3}\big)=4$
Hence, the correct option is (c).
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Between any two rational numbers there.
The area of a triangle whose vertices are (0, 0), (4, 0) and (0, 6) is:
The value of $\frac{2^\circ+7^\circ}{5^\circ}$ is:
→The weight of $10$ students $($in$ \ kg)$ are: $ 55, 40, 35, 60, 38, 36, 45, 31, 44.$
The median weight is:
→The median weight is:
In the given figure, O is the centre of a circle and $\angle\text{AOC}=120^\circ.$ Then, $\angle\text{BDC}=?$
→→- 60°
- 45°
- 30°
- 15°
If the perimeter of an equilateral triangle is 180cm. Then its area will be:
If $x + a$ is a factor of $x^4 - a^2x^2 + 3x - 6a,$ then $a =$
→The diameter of the base of a cylinder of curved surface area $88\ cm^2$ and height $14\ cm$ is:
→