Question

Solve
$\frac{743\times 743\times 743+257\times 257\times 257}{743\times 743-743\times 257+257\times 257}$

Answer 1

$\frac{743\times 743\times 743+257\times 257\times 257}{743\times 743-743\times 257+257\times 257}$

$\frac{(743{)}^3+(257{)}^3}{(743{)}^2-743\times 257+(257{)}^2}$

we know $a^3+b^3=(a+b)(a^2-ab+b^2)$

$\Rightarrow \frac{(743+257)\left(\right(743{)}^2-743\times 257+\left(257{)}^2\right)}{\left[\right(743{)}^2-743\times 257+\left(257{)}^2\right]}$

$\Rightarrow 743+257=1000$