Question

Обчислити значення виразу. З поясненням

Answer 1

$\frac{77^{3}-69^{3}}{70^{2}-62^{2}} -\frac{77^{3}+41^{3}}{125^{2} -7^{2}}-\frac{1}{2}=\frac{(77-69)(77^{2}+77*69+69^{2})}{(70-62)(70+62)} -\frac{(77+41)(77^{2}-77*41+41^{2})}{(125-7)(125+7)}-\frac{1}{2}=\frac{8*(77^{2}+77*69+69^{2})}{8*132} -\frac{118*(77^{2}-77*41+41^{2})}{118*132}-\frac{1}{2}=\frac{77^{2}+77*69+69^{2}-77^{2}+77*41-41^{2}}{132}-\frac{1}{2}=\frac{77(69+41)+(69-41)(69+41)}{132}-\frac{1}{2}=\frac{77*110+28*110}{132}-\frac{1}{2}=\frac{110*((77+28)}{132}-\frac{1}{2}=$

$=\frac{110*105-66}{132}=\frac{11484}{132}=87$

Answer 2

87

Объяснение:

(77³-69³)/(70²-62²) -(77³+41³)/(125²-7²) -1/2=((77-69)(77²+77·69+69²))/((70-62)(70+62)) -((77+41)(77²-77·41+41²))/((125-7)(125+7)) -1/2=(8·(77²+77·69+69²))/(8·132) -(118·(77²-77·41+41²))/(118·132) -1/2=(77²+77·69+69²-77²+77·41-41²)/132 -1/2=(77·(69+41)+(69²-41²))/132 -1/2=(77·(69+41)+(69-41)(69+41))/132 -1/2=((69+41)(77+28))/132 -1/2=(110·105)/132 -1/2=(5·35)/2 -1/2=(175-1)/2=174/2=87