Question
If $\Big(\text{x}+\frac{1}{\text{x}}\Big)=4$ Find the values of:
$\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)$
$\Big(\text{x}^2+\frac{1}{\text{x}^2}\Big)$
✓
Answer
$\Big(\text{x}+\frac{1}{\text{x}}\Big)=4$
Squaring on both sides:
$\Big(\text{x}+\frac{1}{\text{x}}\Big)^2=(4)^2$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}+2\times\text{x}+\frac{1}{\text{x}}=16$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}+2=16$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}=16-2=14$
$\therefore\text{x}^2+\frac{1}{\text{x}^2}=14$
Squaring on both sides:
$\Big(\text{x}+\frac{1}{\text{x}}\Big)^2=(4)^2$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}+2\times\text{x}+\frac{1}{\text{x}}=16$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}+2=16$
$\Rightarrow\text{x}^2+\frac{1}{\text{x}^2}=16-2=14$
$\therefore\text{x}^2+\frac{1}{\text{x}^2}=14$
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
A man saves 18% of his monthly income. If he saves Rs. 1890 per month, what is his monthly income?
The curved surface area of a cylindrical pillar is $264 m^2$ and its volume is $924 m^3$. Find the diameter and height of the pillar.
→If 9 girls can prepare 135 garlands in 3 hours, how many girls are needed to prepare 270 garlands in 1 hour?
The sides of a rectangle are the ratio 4 : 5. Find its sides if the perimeter is 90cm.
Look at the histogram given below and answer the question that follow:
- What information is being given by the histogram?
- How many teachers are of age less than 45 years?
- How many teachers are of age 40 years or more but less than 55 years?
Find the cube root of each of the following natural numbers:
2744
2744
Evaluate $\sqrt[3]{4096}$
→The salary of an officer is increased by 25%. By what percent should the new salary be decreased to restore the original salary?
A shepherd has 200 sheep with him. Find the number of sheeps with him after 3 years if the increase in number of sheeps is 8% every year.
A field is in the form of a right triangle with hypotenuse 50m and one side 30m. Find the area of the field.