1) x1 = 8; x2 = 2
2) x1 = 3; x2 = -1
3) x = 2/3
Объяснение:
1) -x^2 + 10x - 16 = 0 (*(-1))
x^2 - 10x + 16 = 0
по т. Виета
x1 + x2 = 10 x1 = 8
x1 * x2 = 16 → x2 = 2
Или через дискриминантD = (-10)^2 - 4 * 1 * 16 = 100 - 64 = 36 (6^2)
x1 = (10+6)/2 = 16/2 = 8
x2 = (10-6)/2 = 4/2 = 2
2) -2x^2 + 4x + 6 = 0 (*(-1))
2x^2 - 4x - 6 = 0
D = (-4)^2 - 4 * 2 * (-6) = 16 + 48 = 64 (8^2)
x1 = (4+8)/2*2 = 12/4 = 3
x2 = (4-8)/2*2 = -4/4 = -1
3) 9x^2 - 12x + 4 = 0
D = (-12)^2 - 4 * 9 * 4 = 144 - 144 = 0
x = 12/2*9 = 12/18 = 2/3
4x-5<-45-4x
4x+4x<-45+5
8x<40
x<5
x∈(-∞;5)