Решите уравнение; (3х+4)(4х-3)-5=(2х+5)(6х-7)

Question

Алгебра: Решите уравнение; (3х+4)(4х-3)-5=(2х+5)(6х-7)

Аня1ove · Accepted Answer

1)2 cos2x=7 cos(π-x)
2Сos2x = -7Cosx
2(2Cos²x - 1) +7Cosx = 0
4Cos²x -2 +7Cosx = 0
Cosx = t
4t² +7t -1 = 0
D =49+16 = 65
t=(-7+√65)/4    t = (-7 -√65)/4
Cosx = (-7+√65)/4    Cosx =  (-7-√65)/4
x = +-arcCos (-7+√65)/4 +2πk , k ∈Z   ∅

2)cos2x=7sin(π-x)
Cos2x = 7Sinx
1 - 2Sin²x -7Sinx = 0
Sinx = t
-2t² -7t +1 = 0
D = 49 +8 = 57
t = (7+√57)/-4 t =(7 -√57)/-4
Sinx = (7+√57)/-4 Sinx = (7-√57)/-4
∅ x = (-1)^n arcSin(7-√57)/-4 +nπ, n∈Z
3) = 2)

MOGZ ответил