11sin^2 a + 9cos^2 a + 8sin^4 a + 2cos^4 a = = 9sin^2 a + 9cos^2 a + 2sin^2 a + 6sin^4 a + 2(sin^4 a + 2cos^4 a) = (*) Заметим, что 1) 9sin^2 a + 9cos^2 a = 9(sin^2 a + cos^2 a) = 9 2) sin^4 a + cos^4 a = sin^4 a + 2sin^2 a*cos^2 a + cos^4 a - 2sin^2 a*cos^2 a = = (sin^2 a + cos^2 a)^2 - 2sin^2 a*cos^2 a = 1 - 1/2*(4sin^2 a*cos^2 a) Подставляем (*) = 9 + 2sin^2 a + 6sin^4 a + 2 - 4sin^2 a*cos^2 a = = 11 + 4sin^2 a - 2sin^2 a + 6sin^4 a - 4sin^2 a*cos^2 a = = 11 - 2sin^2 a + 6sin^4 a + 4sin^2 a*(1 - cos^2 a) = = 11 - 2sin^2 a + 6sin^4 a + 4sin^4 a = 11 - 2sin^2 a + 10sin^4 a = = 10(sin^4 a - 2*1/10*sin^2 a + 1/100) - 1/10 + 11 = = 10(sin^2 a - 1/10)^2 + 109/10 Минимальное значение квадрата равно 0, а всего выражения 109/10.
4x^2-4x+1=35+2|2x-1|
(2x-1)^2-2|2x-1|-35
|2x-1|=t>0 (2x-1)^2=t^2
t^2-2t-35=0
по виету корни: t1=7 t2=-5<0(не подх)
|2x-1|=7
2x-1=7
x=4
2x-1=-7
x=-3