Question

обчислить простым способом

Answer 1

$tt bigg(cfrac{79^3-41^3}{38}+79cdot41bigg):(133.5^2-58.5^2) =\\\= bigg(cfrac{(79-41)(79^2+79cdot41+41^2)}{38}+79cdot41bigg):(133.5^2-58.5^2) =\\\ = bigg(cfrac{38(79^2+79cdot41+41^2)}{38}+79cdot41bigg):(133.5-58.5)(133.5+58.5)=\\\=(79^2+79cdot41+41^2+79cdot41):(75cdot192)=\\\=cfrac{(79+41)^2}{75cdot192}= cfrac{120^2}{75cdot192}=cfrac{(2^3cdot3cdot5)^2}{5^2cdot3cdot2^6cdot3}=cfrac{2^6cdot3^2cdot5^2}{5^2cdot3^2cdot2^6}=1$