(4-x^2)(4+x^2)=(2-x^2)(2+x^2)(4+x^2)
a^2(b-1)-(b-1)=(b-1)(a^2-1)=(b-1)(a-1)(a+1)
(a^2-1)(a^2+1)=(a-1)(a+1)(a^2+1)
b(x^2-4)-(x^2-4)=(x^2-4)(b-1)=(x-2)(x+2)(b-1)
9a^2(a-b)-(a-b)=(a-b)(9a^2-1)=(a-b)(3a-1)(3a+1)
y^2(y-5)-16(y-5)=(y-5)(y^2-16)=(y-5)(y-4)(y+4)
дай побратски лучший ответ
<span>x^2-16X+64=0
D=(-16)^2-4*1*64=256-256=0
т.к дискриминант равен нулю,то уравнение имеет один корень
х=16+0/2=8
</span>
1) sinx - (1 - sin^2(x)) - sin^2(x) = 0
sinx - 1 + sin^2(x) - sin^2(x) = 0
sinx = 1
x = 2πk, k∈Z
2) sinx = t ∈[-1;1]
6t^2 + t - 1 = 0, D=1+4*6 = 25
t1 = (-1-5)/12 = -6/12 = -1/2, sinx = -0.5, x = π/6 + 2πk и x = 5π/6 + 2πk, k∈Z
t2 = (-1+5)/12 = 4/12 = 1/3, sinx = 1/3, x = arcsin(1/3) + 2πk и x = π - arcsin(1/3) + 2πk, k∈Z
3) 1 - sin^2(x) - 4sinx + 3 = 0
-sin^2(x) - 4sinx + 4 = 0
sin^2(x) + 4sinx - 4 = 0
sinx = t ∈[-1;1]
t^2 + 4t - 4 = 0, D=16+16=32
t1 = (-4-√32)/2 < -1
t2 = (-4+√32)/2, x = arcsin((-4+√32)/2) + 2πk и x = π - arcsin((-4+√32)/2) + 2πk
4) sinx*(√3*sinx - 3cosx) = 0
sinx = 0, x = πk
tgx = √3, x = π/3 + πk
5) 2sin^2(x) - √3*2sinx*cosx = 0
2sinx*(sinx - √3*cosx) = 0
sinx = 0, x = πk
tgx = √3, x = π/3 + πk