1.
216х² - 6у⁴ = 6 * (36х² - у⁴) = 6*(6х - у²)(6х + у²) (ответ Е),
2.
а)
S = 6а² = 6*(3х - 4)² = 6*(9х² - 24х + 16) = 54х² - 144х + 96,
б)
V = а³ = (3х - 4)³ = 27х³ - 108х² + 144х - 16,
3.
4,3² - 2,58 + 0,3² = 4,3² - 2*4,3*0,3 + 0,3² = (4,3 - 0,3)² = 4² = 16,
(44² - 12²) / (56² - 16²) = (44 - 12)(44 + 12) / (56 - 16)(56 + 16) =
= (32*56) / (40*72) = 28/45,
4.
1 число - х,
2 число - (х-52),
х² - (х-52)² = 208,
х² - х² + 104х - 2704 = 208,
104х = 208 + 2704,
104х = 2912,
х = 28 - 1 число,
х-52 = 28 - 52 = -24 - 2 число
f(-x) = 2tg(-5x) = -2 tg(5x) нечётная
Период функции: T = π/5
2) 2sin(x+2) = -√3
sin(x+2) = -√3/2
x + 2 = (-1)^n*arcsin(-√3/2) + πn, n∈Z
x + 2 = (-1)^(n+1)*arcsin(√3/2) + πn, n∈Z
x + 2 = (-1)^(n+1)*(π/3) + πn, n∈Z
x = (-1)^(n+1)*(π/3) - 2 + πn, n∈Z
3) 4sinx+7cosx = 0 /cosx ≠ 0
4tgx + 7 = 0
tgx = - 7/4
x = arctg(-7/4) + πk, k∈Z
x = - tg(7/4) + πk, k∈Z
4) 6tg^2x - tgx - 1 = 0
D = 1 + 4*6*1 = 25
a) tgx = (1-5)12
tgx = - 1/3
x1 = - arctg(1/3) + πn, n∈Z
б) tgx = (1+5)/12
tgx = 1/2
x2 = arctg(1/2) + πk, k∈Z
5) (cos4x - cos2x)/sinx = 0.
cos4x - cos 2x = 0; sinx ≠ 0, x1 ≠ πn, n∈Z
2*[sin(4x+2x)/2 * sin(2x-4x)/2] = 0
sin3x * sin x = 0
a) sin3x = 0
3x = πk, k∈Z
x2 = (πk)/3, k∈Z
б) sinx ≠ 0
ответ: x = (πk)/3 , k∈Z
6) Решите неравенство 1-cos2x < 0.
cos2x > 1
2x = 2πm, m∈Z
x = πm, m∈Z
1.
216х² - 6у⁴ = 6 * (36х² - у⁴) = 6*(6х - у²)(6х + у²) (ответ Е),
2.
а)
S = 6а² = 6*(3х - 4)² = 6*(9х² - 24х + 16) = 54х² - 144х + 96,
б)
V = а³ = (3х - 4)³ = 27х³ - 108х² + 144х - 16,
3.
а)
4,3² - 2,58 + 0,3² = 4,3² - 2*4,3*0,3 + 0,3² = (4,3 - 0,3)² = 4² = 16,
б)
(44² - 12²) / (56² - 16²) = (44 - 12)(44 + 12) / (56 - 16)(56 + 16) =
= (32*56) / (40*72) = 28/45,
4.
1 число - х,
2 число - (х-52),
х² - (х-52)² = 208,
х² - х² + 104х - 2704 = 208,
104х = 208 + 2704,
104х = 2912,
х = 28 - 1 число,
х-52 = 28 - 52 = -24 - 2 число