Решение7/7-х. + х^2+49/х^2-49 при х= - 14.
7/(7 - х). + (х^2 + 49)/(х^2 - 49) = 7 / (7 - x) - (x² + 49) / [(7 - x)*(7 + x)] == [7*(7 + x) - x² + 49] / [(7 - x)*(7 + x)] = [49 + 7x - x² - 49] / [(7 - x)*(7 + x)] == [x*(7 - x)] / [(7 - x)*(7 + x)] = x / (7 + x)при х= - 14. - 14 / (7 - 14) = - 14/(-7) = 2
Решение
№ 104.
(tg³x - tg³y) / [(1 + tgxtgy)(tg²x + tgxtgy + tg²y)] =
= [(tgx - tgy)*(tg²x + tgxtgy + tg²y)] / [(1 + tgxtgy)(tg²x + tgxtgy + tg²y)] =
= (tgx - tgy) / (1 + tgxtgy) = tg(x - y)
№105.
(cos⁴2a - sin⁴2a) / (cos4a) - (cos2a - sin2a)² =
= [(cos²2a - sin²2a) * (cos²2a + sin²2a)] / (cos4a) - (cos²2a - 2sin2acos2a + sin²2a) = (cos²2a - sin²2a) / cos4a - 1 + 2sin2acos2a =
= cos4a / cos4a -1 + sin4a = 1 - 1 + sin4a = sin4a
№ 106.
[ 1/(1 - tgx) - 1/(1 + tgx)] * (cos²x - sin²x) =
= (1 + tgx - 1 + tgx)*cos2x / (1 - tg²x) =
= [2tgx*(1 - tg²x)] (1 - tg²x)(1 + tg²x)] = 2tgx / (1 + tg²x) = sin2x
Х(-5х+9)<span>>0
далее смотри фото
Ответ х</span>∈(0,1 4/5)