Question
If $\text{x}^2+\frac{1}{\text{x}^2}=102,$ then $\text{x}-\frac{1}{\text{x}}=$
✓
Answer
- 10
Solution:
$\Big(\text{x}-\frac{1}{\text{x}}\Big)^2=\text{x}^2+\frac{1}{\text{x}^2}-2(\text{x})\frac{1}{\text{x}}$
$\Big(\text{x}-\frac{1}{\text{x}}\Big)^2=\text{x}^2+\frac{1}{\text{x}^2}-2$
$=102-2$ $\Big\{\text{x}^2+\frac{1}{\text{x}^2}=102\Big\}$
$=100$
$\Rightarrow\text{x}-\frac{1}{\text{x}}=\sqrt{100}$
$\Rightarrow\text{x}-\frac{1}{\text{x}}=10$
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
In $\triangle\text{PQR},\ \angle\text{P} = 60^\circ,\ \angle\text{Q} = 50^\circ.$ Which side of the triangle is the longest?
→If $\bar{\text{x}}_1, \bar{\text{x}}_2, \bar{\text{x}}_3, ....., \bar{\text{x}}_\text{n}$ are the means of $n$ group with $n_1, n_2, ...., nn$ number of observations respectively, then the mean $\bar{\text{x}}$ of all the groups taken together is given by:
→If one angle of a parallelogram is 24º less than twice the smallest angle, then the measure of the largest angle of the parallelogram is:
A cube of side $4\ cm$ contains a sphere touching its sides. Find the approximate volume of the gap in between.
→The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former. The ratio of their radii is:
The number of planes passing through 3 non-collinear points is:
- 4
- 3
- 2
- 1
The abscissa of any point on y-axis is:
- 0
- 1
- -1
- Any number
If $\sqrt2=1.4142,$ then $\sqrt{\frac{\sqrt2-1}{\sqrt2+1}}$ is equal to:
→→-
0.1718
-
5.8282
-
0.4142
-
2.4142
A conical tent is $21\ m$ high and the diameter of its base is $4\ m.$ If $10$ men sleep in it, then the average number of cubic dm of air space per man is:
→