Abhijit Guha Solutions for Chapter: Elementary Algebra, Exercise 2: Practice Problems Level 2

If $x=3+2\sqrt{2}$ and $xy=1$, then the value of $\frac{x^2+3xy+y^2}{x^2-3xy+y^2}$ is:

If $\mathrm{a}+\mathrm{b}+\mathrm{c}=0$, then the value of $\left(\frac{\mathrm{a}+\mathrm{b}}{\mathrm{c}}+\frac{\mathrm{b}+\mathrm{c}}{\mathrm{a}}+\frac{\mathrm{c}+\mathrm{a}}{\mathrm{b}}\right)\left(\frac{\mathrm{a}}{\mathrm{b}+\mathrm{c}}+\frac{\mathrm{b}}{\mathrm{c}+\mathrm{a}}+\frac{\mathrm{c}}{\mathrm{a}+\mathrm{b}}\right)$ is:

If $a, b, c$ are non-zero $a+\frac{1}{b}=1$ and $b+\frac{1}{c}=1$, then the value of $abc$ is:

If $a+b+c=2s$, then $\frac{(s-a{)}^2+(s-b{)}^2+(s-c{)}^2+s^2}{a^2+b^2+c^2}$ is equal to:

If $x\left(3-\frac{2}{x}\right)=\frac{3}{x}$, then the value of $x^2+\frac{1}{x^2}$ is:

If ${\mathrm{x}}^4+\frac{1}{{\mathrm{x}}^4}=119$ and $\mathrm{x}>1$, then find the positive value of ${\mathrm{x}}^3-\frac{1}{{\mathrm{x}}^3}$:

If $x^2+y^2+1=2x$, then the value of $x^3+y^5$ is:

If $ab+bc+ca=0$, then the value of $\frac{1}{a^2-bc}+\frac{1}{b^2-ac}+\frac{1}{c^2-ab}$: