Х1²-x2²=11
x1=6
x2=5
Проверка : 36-25=11.
180 градусов - 70 градусов = 110 градусов
Ответ: 110 градусов
1) log₃x * (5 - 2log₃x) = 3
5log₃x - 2log₃²x = 3
2log₃²x - 5log₃x + 3 = 0
log₃x = t
2t² - 5t + 3 =0
t₁ = 1
t₂ =
log₃x = 1
x = 3log₃x =
x = Ответ: 3 ;
2) log₂²x + 3log₁/₂x + 2 =0
log₂²x + 3*
+ 2 = 0
log₂²x - 3log₂x + 2 =0
log₂x = t
t² - 3t + 2 =0
t₁ = 1
t₂ = 2
log₂x = 1
x = 2log₂x = 2
x = 4Ответ: 2; 4
3) (1/2log₃x - 6 )*log₉x = 4(2-log₉x)
(1/2log₃x - 6) *
log₃x = t
t² - 12t = 32 - 8t
t² - 4t - 32 = 0
D₁ = 4+32=36
t₁ = 8
t₂ = -4
log₃x = 8
x = log₃x = -4
x = 4) log₂x * log₃x = 4log₃2
log₃x = 2log₃2 log₃x = -2log₃2
log₃x = log₃4 log₃x = log₃
x=4 x = 5) lg²x + 4 = 2*2*lgx
lg²x - 4lgx + 4 = 0
lgx = t
t² - 4t + 4=0
D₁ = 4-4=0
t = 2
lgx = 2
x = 100
Поскольку x=-4 ∈ [-10; 0], то f(-4) = -4 · (-4) = 16.
Ответ: f(-4) = 16.
ОДЗ
x+3>0
x+2>0
x>-2
log12 (x+3) + log12 (x+2)=1
log 12 ((x+3)(x+2)) = log12 (12)
(x+3)(x+2)=12
x^2 +5x-6=0
x1=-6 не удовл. ОДЗ
x2=1