0+(1++cos6x)/2-(1+cos8x)/2=0
-(cos8x-cos6x)=0
2sin7xsinx=0
sin7x=0
7x=πk sinx=0
x=πk/7 x=πkx
2)1-cos6x+1-cos8x+1-cos12x+1-cos14x=4
-(cos6x+cos14x)-(cos8x+cos12x)=0
2cos10xcos4x-2cos10xcos2x=0
cos10x(cos4x+cos2x)=0
x=π/20+πk/10
cos3xcosx=0
x=π/6+πk
x=π/2+πk
4^x * 1/4 + 2^x * 1/4 - 3/2 ≥ 0
4^x + 2^x - 6 ≥ 0
2^x = t
t^2 + t - 6 ≥ 0
t^2 + t - 6 = 0
D = 1 + 4*6 = 25
t1 = ( - 1 + 5)/2 = 2
t2 = ( - 1 - 5)/2 = - 3
2^x = 2
x = 1
2^x = - 3
нет решений
x ∈ [1; + ∞)
<span>(m-n)^2+2n(m-n)+n^2=м^2-2mn+n^2+2mn+2n^2+n^2=m^2-4nm+4n^2=(m-2n)^2</span>
Это элементарное тригонометрическое уравнение
sin y = 0,5
y1 = pi(8x - 3)/6 = pi/6 + 2pi*k, наиб. отр. корень pi/6 - 2pi = -11pi/6
8x - 3 = -11; 8x = -8; x = -1
y2 = pi(8x - 3)/6 = 5pi/6 + 2pi*k, наиб. отр. корень 5pi/6 - 2pi = -7pi/6
8x - 3 = -7; 8x = -4; x = -1/2
Ответ: -1/2