Algebra Questions

If the average of $x$ and $\frac{1}{x}$ ($x\ne 0$) is $m$, then the average of $x^2$ and $\frac{1}{x^2}$ is :

The ratio of the sums of money Arun and Ahaan had is $9:5$. If Arun gives ₹$12$ from his share to Ahaan, then the ratio will change to $4:3$. How much money did Arun have initially?

Name the person who had a major influence in the field of Algebra in India.

The sum of two numbers is $15$. If the sum of their reciprocals is $\frac{3}{10}$, then find the two numbers?

Two numbers are in the ratio $5:8$. If $4$ is added to each, the ratio becomes $2:3$. Find the smaller number.

The LCM of two numbers is $12$ times their HCF. The sum of HCF and LCM is $1560$. If one of the numbers is $120$, then find the other number.

Simplify the following expression:
0.7+0.4
0.7
2
+(0.4+0.2)(0.7)+(0.4×0.2)
​

If the semi-perimeter and area of a rectangular field whose length and breadth are 'x' and 'y' is 12cm and 28cm
2
, respectively, then find the value of x
4
+x
2
y
2
+y
4
.