Question

Evaluate :
$$\frac{0.8\times 0.8\times 0.8+0.5\times 0.5\times 0.5}{0.8\times 0.8-0.8\times 0.5+0.5\times 0.5}$$

Answer 1

$\frac{0.8\times 0.8\times 0.8+0.5\times 0.5\times 0.5}{0.8\times 0.8-0.8\times 0.5+0.5\times 0.5}$
Let $0.8=a$ and $0.5=b$
Then, the given expression becomes
$\frac{a\times a\times a+b\times b\times b}{a\times a-a\times b+b\times b}$
$=\frac{a^3+b^3}{a^2-ab+b^2}$
$=\frac{(a+b)(a^2-ab+b^2)}{a^2-ab+b^2}$
$=a+b$
$=0.8+0.5$
$=1.3$