8. 1-Б; 2-Г; 3-А; 4-В.
9. 1-Д; 2-Б; 3-Г; 4-А.
Подробнее объяснение:
8. 1) 2cosx = 1
cosx = 1/2
x = ± arccos1/2 + 2πn, n є Z
x = ± π/3 + 2πn, n є Z. Б.
2) 2cosx/2 = 1
cosx/2 = 1/2
x/2 = ± arccos1/2 + 2πn, n є Z
x/2 = ± π/3 + 2πn, n є Z.
x = ± 2π/3 + 4πn, n є Z. Г.
3) cos2x = 1
2x = ± arccos1/2 + 2πn, n є Z
2x = ± π/3 + 2πn, n є Z.
x = ± π/6 + πn, n є Z. А.
4) cosx/2 = 1
x/2 = 2πn, n є Z.
x = 4πn, n є Z. В.
Відповідь: 1-Б; 2-Г; 3-А; 4-В.
9. 1) sin2x = 0. [0; 2π] sinx є [-1; 1]
2x = πn, n є Z
x = πn/2, n є Z n = 0, x = 0 +
n = 1, x = π/2. +
n = 2, x = π +
n = 3, x = 3π/2 +
n = 4, x = 2π. +
n = 5, x = 5π/2 -
П'ять коренів. Д.
2) sin2x = 1. [0; 2π]
2x = π/2 + 2πk, k є Z.
x = π/4 + πk, k є Z.
k = 0, x = π/4. +
k = 1, x = 5π/4. +
k = 2, x = 9π/4. -
Два корені. Б.
3) cos2x = 0. [0; 2π]
2x = π/2 + πm, m є Z.
x = π/4 + πm/2, m є Z.
m = 0, x = π/4. +
m = 1, x = 3π/4. +
m = 2, x = 5π/4. +
m = 3, x = 7π/4. +
m = 4, x = 9π/4. -
Чотири корені. Г.
4) tgx/2 = 1. [0; 2π]
x/2 = arctg1 + πt, t є Z.
x/2 = π/4 + πt, t є Z.
x = π/2 + 2πt, t є Z.
t = 0, x = π/2 . +
t = 1, x = 5π/2. -
Один корінь. А.
Відповідь: 1-Д; 2-Б; 3-Г; 4-А.
1. х² + 4х - 5 = 0
a=1 b=4 c=-5
x0= -b/2a= -4/2×1= -4/2= -2
y0= y(x0) = (-2)²+4×(-2)-5 = -9
ответ: -2 и -9
2. x² - 8x - 9 = 0
a=1 b=-8 c=-9
x0= -b/2a = 8/2×1 = 4/2 = 2
y0= y(x0) = 2²-8×2-9 = -21
ответ: 2 и 21
3. x² + x - 6 = 0
a= 1 b=1 c=-6
x0= -b/2a = -1/2×1 = -1/2= -0,5
y0= y(x0) = -0,5²+0,5-6 = -5,75
ответ: -0,5 и -5,75
4. х² - 6x - 7 = 0
a= 1 b=-6 c=-7
x0= -b/2a= -6/2×1= -6/2= -3
y0= y(x0) = -3²-6×(-3)-7= 2
ответ: -3 и 2
5. x² + 6x - 40 = 0
a=1 b= 6 c=-40
x0= -b/2a= -6/2×1= -6/2= -3
y0= y(x0) = -3²+6×(-3)-40 = -67
ответ: -3 и -67
6. x² - x - 2 = 0
a=1 b=-1 c=-2
x0= -b/2a= 1/2×1 = 1/2 = 0,5
y0= y(x0) = 0,5²-0,5-2 = -2,25
ответ: 0,5 и -2,25
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