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

If $\left(5\sqrt{5}{x}^3-3\sqrt{3}{y}^3\right)÷\left(\sqrt{5}x-\sqrt{3}y\right)=\left(A{x}^2+B{y}^2+Cxy\right)$, then what is the value of $\left(3A-B-\sqrt{15}C\right)$?

If $x+y+z=19, x^2+y^2+z^2=133$ and $xz=y^2, x>z>0$, what is the value of $\left(x-z\right)$?

If $x^2-4x+1=0$, then what is the value of $\left(x^6+x^{-6}\right)$?

If ${\left(x^3+\frac{1}{x^3}-k\right)}^2+{\left(x+\frac{1}{x}-p\right)}^2=0$, where $k$ and $p$ are real numbers and $x\ne 0$, then $\frac{k}{p}$ is equal to _____.

If $x^4+x^2{y}^2+y^4=133$ and $x^2-xy+y^2=7$, then what is the value of $xy$?

If $x=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}, y=\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$, then $\left(x+y\right)$ is _____

If $a=b^x, b=c^y$ and $c=a^z$, then the value of $xyz$ is:

If $x^3+y^3=72$ and $xy=8$, $(x > y)$, then find the value of $(x-y)$.