Объяснение:
9.
log₆(x²+6x)-3<0
log₆(x²+6x)<3
log₆(x²+6x)<log₆6³
log₆(x²+6x)<log₆216
x²+6x<216
x²+6x-216<0
x²+6x-216=0 D=900 √D=30
x₁=-18 x₂=12
(x+18)(x-12)<0 ⇒ x∈(=18;12).
ответ: С.
10.
{3^y=27^x {3^y=3^(3x) {y=3x
{log₂(y-x²)=1 {log₂(y-x²)=log₂2 {y-x²=2 {3x-x²=2
x²-3x+2=0 D=1
x₁=1 y=3*1=3 y₁=3
x₂=2 y=3*2=6 y₂=6.
ответ: x₁=1 y₁=3 x₂=2 y₂=6.
11.
{x²+x-6<0 {x²+x-6=0 D=25 √D=5 x₁=-3 -1/16)(x₂=2 (x+3)(x-2)<0 -∞__+__-3__-__2__+__+∞ x∈(-3;2)
{log₄²x-log₄x-6<0
Пусть log₄x=t.
t²-t-6<0
t²-t-6=0 D=25 √D=5
t₁=log₄x=3 x=4³ x₁=64.
t₂=log₄x=-2 x=4⁻² x₂=1/16
(x-1/16)(x-64)<0 ∞__+__1/16__-__64__+__+∞
x∈(1/16;64). ⇒ x∈(1/16;2).
ответ: D.
1.
а) 2x²/14x = x/7
б) 2x-8/3x-12 = 2(x-4)/3(x-4) = 2/3
в) 14a/21ab = 2/3b
г) 8m²n/12mn² = 2m/3n
д) 4m-4n/8mn = 4(m-n)/8mn = m-n/2mn
е) 12ab/6a-6b = 12ab/6(a-b) = 2ab/a-b
ж) x²-4/(x-2)² = (x-2)(x+2)/(x-2)² = x+2/x-2
з) 2x-1/(2x-1)² = 1/2x-1
и) 12ab(x-1)/24a(1-x) = b(x-1)/-2(x-1) = -b/2
2.
а) 5/3x и 7/6
10/6x и 7x/6x
б) 2/5x и 1/20x
8/20x и 1/20x
в) 4/x-6 и x/2x-12
8/2x-12 и x/2x-12
г) 4/x-6 и x/6-x
4/x-6 и -x/x-6
д) x/x+5 и 5/x²-25
x²-5x/x²-25 и 5/x²-25
е) x/4x+x² и 4/3x+12
x/x(4+x) и 4/3(x+4)
3x/3x(4+x) и 4x/3x(4+x)
3x/12x+3x² и 4x/12x+3x²
ж) x/1-x² и x/x+1
x/1-x² и x(x-1)/1-x²
x/1-x² и x²-x/1-x²
з) 2/x²+4x+4 и x/x+2
2/(x+2)² и x(x+2)/(x+2)²
2/(x+2)² и x²+2x/(x+2)²
1) √x> -2
(√x)²>(-2)²
x>4
ответ: (4;+∞)
3) b₁= 0,5/0,25=2