Jitender Gupta and Divya Malik Solutions for Exercise 3: CHAPTER EXERCISE

Find the mean proportional between:

$\left(\sqrt{27}-\sqrt{18}\right)\mathrm{and} \left(\sqrt{27}+\sqrt{18}\right)$.

Find the third proportional to

$16$ and $36$.

The third proportional to ${\left(x^2+y^2+xy\right)}^2$ and $\left(x^3-y^3\right)$ is ${\left(x-y\right)}^k$, find $k$.

Find the fourth proportional of the following.

$3a^2{b}^2, a^3, b^3$.

The fourth proportional of $a^2- 5a+6, a^2+a-6, a^2-9$ is ${\left(a+3\right)}^k$, find $k$.

If $7a-15b= 4a+b$, then find the value of $\frac{3a^2+2b^2}{3a^2-2b^2}$.

If $p=\frac{4xy}{x+y}$, then find the value of, $\frac{p+2x}{p-2x}+\frac{p+2y}{p-2y}$.

If $y=\frac{10ab}{a+b}$, then find the value of $\frac{y+5a}{y-5a}+\frac{y+5b}{y-5b}$.