г) (1-9y²) / (3y²-13+4) = (1+3y)(1-3y) / 3(y-4)(y-1/3) = 3(1/3+y)(1/3-y) / 3(y-4)(y-1/3) = (1/3+y)(1/3-y) / (y-4)(y-1/3)
3y²-13+4 = 0;
D = (-13)²-4*3*4 = 169-48 = 121, √D = 11
y₁ = (13+11) / 2*3 = 24/6 = 4
y₂ = (13-11) / 2*3 = 2/6 = 1/3
Значит: 3y²-13+4 = 3(y-4)(y-1/3)
д) (36a²-12a+1) / (6a²+11a-2) = 36(a-1/6)(a-1/6) / 6(a-1/6)(a+2) = 6(a-1/6) / (a+2)
36a²-12a+1 = 0;
D = (-12)²-4*36*1 = 144-144 = 0, √D = 0
a = 12/(2*36) = 12/72 = 1/6
Значит: 36a²-12a+1 = 36(a-1/6)(a-1/6)
6a²+11a-2 = 0;
D = 11²-4*6*(-2) = 121 + 48 = 169, √D = 13
a₁ = (-11+13) / 2*6 = 2/12 = 1/6
a₂ = (-11-13) / 2*6 = -24/12 = -2
Значит: 6a²+11a-2 = 6(a-1/6)(a+2)
x = πk/4 - π/48
x = 3π/4 + πk
Объяснение:
cos3x - sin5x = √3 (cos5x + sin3x)
cos3x - sin5x = √3 cos5x + √3 sin3x
cos3x - √3 sin3x = sin5x + √3 cos5x
2*(1/2cos3x - √3/2 sin3x ) = 2*(1/2sin5x + √3/2 cos5x)
1/2cos3x - √3/2 sin3x = 1/2sin5x + √3/2 cos5x
sin(30° - 3x) = sin(5x + 60°)
sin(30° - 3x) - sin(5x + 60°) = 0
2sin( ((30° - 3x) - (5x + 60°))/2)*cos(((30° - 3x)+ (5x + 60°))/2) = 0
2sin(-4x-15°)cos(-x + 45°) = 0
-2sin(4x + π/12)cos(x - π/4) = 0
1) sin(4x + π/12) = 0
4x + π/12 = πk
4x = πk - π/12
x = πk/4 - π/48
2) cos(x - π/4) = 0
x - π/4 = π/2 + πk
x = π/2 + πk + π/4
x = 3π/4 + πk
