S3: which kind of sports is your favourite? S1: Oh, I lobe hockey. I know everything about it. It's a winter sport, but simetimes people play it even when it's summer or autumn. S3: and you, S2? S2: well, I hate hockey. It's very dangerous to play in it, though sometimes games can be quite interesting. I love swimming. It's great to swim and relax in the same time. I love this feeling of relaxing and training [in the same time]. S1: oh, and you, S3? Which kind of sports do you prefer? S3: Frankly speaking, I like sport(s) but I didn't really know what I should choose. Can you help with that choice? S1: Yes, of course. Let's talk about it a bit later. S3+S2: Ok. See you then(,)guys. Bye.
Чтобы уравнение x² + 2(a+1)*x + 9 = 0 имело 2 разных положительных корня надо в общем виде : приведенное квадратное уравнение вида х² + b₁x + c₁= 0 имеет 2 положительных корня x₁ и x₂, если выполняются 3 условия 1) x₁*x₂ = c₁ > 0 - в нашем примере c₁ = 9 2) x₁+ x₂ = -b₁ > 0 - в нашем примере -b₁ = -(2(a+1)) -2a -2 > 0 ; a < -1 3) Дискриминант D = b₁² - 4c₁ > 0 - в нашем примере D = ( -(2(a+1)) )² - 4*9 D = (2a + 2 - 6) * (2a + 2 + 6) = (2a - 4) * (2a + 8) >0 (a - 2) * (a + 4) >0 корни -4 и 2, т.е. D>0 при а < -4 и a>2 пересечение множеств из 2) и 3) будет a < -4 Уравнение x² + 2(a+1)*x + 9 = 0 будет иметь два положительных корня при a < -4
(Sin3xCos2x - Cos3xSin2x) / Sim2xCos 2x
уравнение примет вид:
Sinx /Sin2xCos2x = 2/Cos3x
SinxCos3x = 2Sin2xCos2x
1/2*2SinxCos3x = Sin4x
1/2(Sin4x -Sin2x) = Sin4x
1/2Sin4x -1/2Sin2x -Sin4x = 0
-1/2Sin4x -1/2 Sin2x = 0
Sin4x +Sin2x = 0
2Sin3xCosx = 0
a) Sin3x = 0 б) Cos x = 0
3x = πn, nЄ Z x = π/2 + πk,kЄ Z
x = π/3 + πn/3, nЄ Z