Question
If $\text{x}=\sqrt6+\sqrt5,$ then $\text{x}^2+\frac{1}{\text{x}^2}-2=$
✓
Answer
- 20
Solution :
$\text{x}^2+\frac{1}{\text{x}^2}-2=\Big(\text{x}-\frac{1}{\text{x}}\Big)^2$
$\text{x}=\sqrt6+\sqrt5$
$\Rightarrow\frac{1}{\text{x}}=\frac{1}{\sqrt6+\sqrt5}=\frac{1}{\sqrt6+\sqrt5}\times\frac{\sqrt6-\sqrt5}{\sqrt6-\sqrt5}\\ \ =\frac{\sqrt6-\sqrt5}{1}=\sqrt6-\sqrt5$
Now,
$\Big(\text{x}-\frac{1}{\text{x}}\Big)^2=\big[\sqrt6+\sqrt5-\big(\sqrt6-\sqrt5\big]^2\\ \ =\big(2\sqrt5\big)^2=4\times5=20$
Hence, correct option is (d).
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
Surface area of sphere of diameter $14\ cm$ is:
→For which set of data does the median equal the mode?
To know the opinion of the students about the subject Sanskrit, a survey of 200 students was conducted. The data is recorded as under.
What is the probability that a student chosen at random does not like it?
→|
Opinion
|
like
|
dislike
|
|
Number of students
|
135
|
65
|
- $\frac{13}{27}$
- $\frac{27}{40}$
- $\frac{13}{40}$
- $\frac{27}{13}$
Which of the following quadrilateral is not a rhombus?
- All four sides sre equal.
- Diagonals bisect each other.
- Diagonals bisect opposite angles.
- One angle between the diagonals is 60°.
A rational number between -3 and 3 is:
- 0
- -4.3
- -3.4
- 1.101100110001...
A surface of shape has:
In figure, the value of y is:
- 20°
- 30°
- 45°
- 60°
Which of the following is a rational number?
→- $\sqrt{5}$
- 0.101001000100001...
- $\pi$
- 0.853853853...