Question
If $\text{x}^2+\frac{1}{\text{x}^2}=102,$ then $\text{x}-\frac{1}{\text{x}}=$
- 8
- 10
- 12
- 13
✓
Answer
- 10
$\Big(\text{x}-\frac{1}{\text{x}}\Big)^2=\text{x}^2+\frac{1}{\text{x}^2}-2(\text{x})\frac{1}{\text{x}}$
$\Big(\text{x}-\frac{1}{\text{x}}\Big)^2=\text{x}^2+\frac{1}{\text{x}^2}-2$
$=102-2$ $\Big\{\text{x}^2+\frac{1}{\text{x}^2}=102\Big\}$
$=100$
$\Rightarrow\text{x}-\frac{1}{\text{x}}=\sqrt{100}$
$\Rightarrow\text{x}-\frac{1}{\text{x}}=10$
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
Axioms are assumed:
A solid cylinder of radius ‘r’ and height ‘h’ is placed over another cylinder of same height and radius. The total surface area of the shape so formed is:
If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then $\frac{\text{A}}{\text{V}}$.
→In the given figure, $A$ and $B$ are the centres of two circles having radii $5\ cm$ and $3\ cm$ respectively and intersecting at points $P$ and $Q$ respectively. If $AB = 4\ cm,$ then the length of common chord $PQ$ is:
→A metallic sphere of radius 10.5cm is melted and then recast into small cones, each of radius 3.5cm and height 3cm. The number of such cones will be:
If $x + y + z + = 9$ and $xy + yz + zx = 23,$ then the value of $x^3 + y^3 + z^3 - 3xyz$ is:
→If two lines intersect each other then:
If (x, y) = (y, x), then.
Between any two rational numbers there :