MCQ
If $\text{x}=\sqrt5+2,$ then $\text{x}-\frac{1}{\text{x}}$ equals :
- A$2\sqrt5$
- B$4$
- C$2$
- D$\sqrt5$
✓
Answer
- $4$
Solution:
$\text{x}=\sqrt{5}+2$
$\Rightarrow\frac{1}{\text{x}}=\frac{1}{\sqrt5+2}=\frac{1}{\sqrt5+2}\frac{\sqrt5-2}{\sqrt5-2}\\ \ =\frac{\sqrt5-2}{1}=\sqrt5-2$
Now, $\text{x}-\frac{1}{\text{x}}=\sqrt5+2-\big(\sqrt5-2\big)\\ \ =\sqrt5+2-\sqrt5+2=4$
Hence, correct option is (b).
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
$\text{Mode}+\frac{3}{2}(\text{Median - Mode})=$
→Tally marks are used to find:
The diameter of the base of a cone of height 15cm and volume 770cm3 is:
If the volumes of two cones be in the ratio $1: 4$ and the radii of their bases be in the ratio $4: 5$, then the ratio of their heights is
→The value of $\sqrt{3-2\sqrt{2}}$ is:
→- $\sqrt{3}+\sqrt{2}$
- $\sqrt{3}-\sqrt{2}$
- $\sqrt{2}+1$
- $\sqrt{2}-1$
The point (-3, 0) lies.
Write the correct answer in the following: The graph of the linear equation 2x + 3y = 6 cuts the Y-axis at the point,
Euclid’s Postulate 1 is:
Write the correct answer in the following:
In a medical examination of students of a class, the following blood groups are recorded:
A student is selected at random from the class. The probability that he/ she has blood group B, is:
→In a medical examination of students of a class, the following blood groups are recorded:
| Blood group | A | AB | B | O |
| Number of Student | 10 | 13 | 12 | 5 |
- $\frac{1}{4}$
- $\frac{13}{40}$
- $\frac{3}{10}$
- $\frac{1}{8}$