Embibe Experts Solutions for Chapter: Advance Maths, Exercise 1: Exercise 1

If $9\left({\mathrm{a}}^2+{\mathrm{b}}^2\right)+{\mathrm{c}}^2+20=12(\mathrm{a}+2\mathrm{b})$, then the value of $\sqrt{6a+9b+2c}$ is

If $\sqrt{x}-\frac{1}{\sqrt{x}}=\sqrt{7}$ then the value of $x^2+\frac{1}{x^2}$ is:

If $\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{x}}=2, (\mathrm{x},\mathrm{y}\ne 0)$, then the value of $(\mathrm{x}-\mathrm{y})$ is

If $\left(56\sqrt{7}{\mathrm{x}}^3-2\sqrt{2}{\mathrm{y}}^3\right)÷(2\sqrt{7}\mathrm{x}-\sqrt{2}\mathrm{y})={\mathrm{Ax}}^2+{\mathrm{By}}^2-\mathrm{Cxy}$, then find the value of $\mathrm{A}+\mathrm{B}-\sqrt{14}\mathrm{C}.$

If $2{\mathrm{x}}^2-7\mathrm{x}+5=0,$then what is the value of $x^3+\frac{125}{8x^3}?$

If $\left(\mathrm{x}+\frac{1}{\mathrm{x}}\right)=\frac{17}{4}, \mathrm{x}>1$,then what is the value of $\mathrm{x}-\frac{1}{\mathrm{x}}?$

If $x^4-62x^2+1=0$, where $x>0$, then the value of $x^3+x^{-3}$ is:

If ${\left(2x+y\right)}^3-{\left(x-2y\right)}^3=\left(x+3y\right)\left[A{x}^2+B{y}^2+Cxy\right]$, then what is the value of $(A+2B+C)?$