Tg²x - 5 = 4tgx
tg²x - 4tgx - 5 = 0
Пусть tgx = a
a² - 4a - 5 = 0
D = (-4)² - 4*(-5) = 16 + 20 = 36
a₁ = (4 + √36)/2 = (4 + 6)/2 = 5
a₂ = (4 - √36)/2 = (4 - 6)/2 = - 1
tgx₁ = 5 tgx₂ = - 1
x₁ = arctg5 + πn, n ∈ z x₂ = arctg(- 1) + πn, n ∈ z
x₂ = - π/4 + πn, n ∈ z
<span>12-(4-x)²=x(3-x)
12-16+8х-</span> x^{2} =3х- x^{2}
8х-3х+ x^{2} - x^{2} =16-12
5х=4
4
х=⁻⁻⁻
5
х=0,8
Ответ: 0,8
Найдем производную
f ' (x) = 6 (4x + 3)^5 (4x + 3) ' = 24 (4x + 3)^5
f ' (-1) = 24* ( - 4 + 3)^5 = 24 * (-1)^5 = - 24
0 4 5 10 12 200 У
Х 12 16 30