Question

Prove that :

$\frac{0.87\times 0.87\times 0.87+0.13\times 0.13\times 0.13}{0.87\times 0.87-0.87\times 0.13+0.13\times 0.13}=1$

Answer 1

$\frac{0.87\times 0.87\times 0.87+0.13\times 0.13\times 0.13}{0.87\times 0.87-0.87\times 0.13+0.13\times 0.13}$

$=\frac{(0.87{)}^3+(0.13{)}^3}{(0.87{)}^2-0.87\times 0.13+(0.13{)}^2}$

$=\frac{a^3+b^3}{a^2-ab+b^2}$, where $a=0.87$ and $b=0.13$

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

$=a+b=0.87+0.13=1$