Question

Find the following squares by using the identity
${(\frac{x^2}{yz}+\frac{y^2}{xz})}^2$

Answer 1

${(\frac{x^2}{y^2}+\frac{y^2}{x^2})}^2$

we have the identity ${(a+b)}^2=a^2+b^2+2ab$

$\therefore {(\frac{x^2}{y^2}+\frac{y^2}{x^2})}^2={\left(\frac{x^2}{y^2}\right)}^2+{\left(\frac{y^2}{x^2}\right)}^2+2\times \frac{x^2}{y^2}\times \frac{y^2}{x^2}=\frac{x^4}{y^2{z}^2}+\frac{y^4}{x^2{z}^2}+\frac{2xy}{z^2}=\frac{1}{z^2}[\frac{x^4}{y^2}+\frac{y^4}{x^2}+2xy]$

or $\frac{1}{z^2}{[\frac{x^2}{y}+\frac{y^2}{x}]}^2$