Question

Find the compounded ratio of the following: 

(a² - b² ): (a² + b²) and (a⁴ - b⁴ ): (a+ b)⁴ 

Answer 1

Compounded ratio of (a² -b² ): (a² + b² )and(a⁴ -b⁴ ) : (a+ b)⁴ 

=${\displaystyle \frac{{\text{a}}^2-{\text{b}}^2}{{\text{a}}^2+{\text{b}}^2}\times \frac{{\text{a}}^4-{\text{b}}^4}{{(\text{a}+\text{b})}^4}}$

= ${\displaystyle \frac{(\text{a}+\text{b})(\text{a}-\text{b})}{({\text{a}}^2+{\text{b}}^2)}\times \frac{({\text{a}}^2+{\text{b}}^2)({\text{a}}^2-{\text{b}}^2)}{{(\text{a}+\text{b})}^2{(\text{a}+\text{b})}^2}}$

= ${\displaystyle \frac{(\text{a}-\text{b})(\text{a}+\text{b})(\text{a}-\text{b})(\text{a}+\text{b})}{{(\text{a}+\text{b})}^2{(\text{a}+\text{b})}^2}}$

= ${\displaystyle \frac{{\left(\text{a - b}\right)}^2}{{\left(\text{a + b}\right)}^2}}$

Compounded ratio= (a - b)² : (a+ b)²