при x∈(
−
∞
;
7
)
∪
(
11
;
∞
). Решая неравенство x²-18x+77>0
Ответ:
x = π + 2πn, n ∈ Z; -π/2 + 2πk, k ∈ Z.
Объяснение:
4cos²(x/2) + 0,5sinx + 3sin²(x/2) = 3
4cos²(x/2) + 2·0,5sin(x/2)·cos(x/2) + 3sin²(x/2) = 3sin²(x/2) + 3cos²(x/2)
cos²(x/2) + sin(x/2)cos(x/2) = 0
cos(x/2)[cos(x/2) + sin(x/2)] = 0
1) cos(x/2) = 0
x/2 = π/2 + πn, n ∈ Z
x = π + 2πn, n ∈ Z
2) cos(x/2) + sin(x/2) = 0
cos(x/2) = -sin(x/2)
tg(x/2) = -1
x/2 = -π/4 + πk, k ∈ Z
x = -π/2 + 2πk, k ∈ Z
P(x,y) = x^2 + 2x + y^2 - 4y + 5 = x^2 + 2x +1 + y^2 - 4y + 4 = (x+1)^2 + (y-2)^2 ≥ 0, что и требовалось доказать.