Log(2) (x+1)≤1
{x+1>0 {x>-1; {x>-1 (-1;1]
{log(2) (x+1)≤log(2) 2 ; {x+1≤2; {x≤1
Ответ. (-1;1]
{4-x>0
{x+5>0
{-x>-4
{x>-5
{x<4
{x>-5
\\\\\\\\\\\\\\\\\\\\\\\\\\\\
--------- -5 ------------- 4 --------------
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
x∈(-5; 4)
Длина интервала: 4- (-5) =4+5=9
Середина интервала: 9: 2=4,5
Ответ: 4) 4,5.
1) (18a-3a²)/(8a²-48a)=3a(6-a)/8a(a-6)=3a(-1)(a-6)/8a(a-6)=-3/8
2) (8p-40)/(15-3p)=8(p-5)/3(5-p)=8(-1)(5-p)/3(5-p)=-8/3
3) (4-x²)/(10-5x)=(2-x)(2+x)/5(2-x)=(2+x)/5=2/5+x/5=0.4+0.2x
4) (3x+6y)²/(5x+10y)=9(x+2y)²/5(x+2y)=9(x+2y)/5=1.8(x+2y)=1.8x+3.6y
5) (ax+bx-ay-by)/(bx-by)=(x(a+b)-y(a+b))/b(x-y)=(a+b)(x-y)/b(x-y)=(a+b)/b=a/b+1
6) (a²-6a+9)/(27-a³)=(a-3)²/(3-a)(9+3a+a²)=(a-3)²/(-1)(a-3)(9+3a+a²)= =(3-a)/(9+3a+a²)
7) (2a-2b)²/(a-b)=4(a-b)²/(a-b)=4(a-b)=4a-4b
8) (4c+12d)²/(c+3d)=16(c+3d)²/(c+3d)=16(c+3d)=16c+48d
9) (4x²-y²)/(6x-3y)²=(2x-3y)(2x+3y)/9(2x-y)²=(2x+y)/9(2x-y)
10) (ab-3b-2a+6)/(15-5a)=(b(a-3)-2(a-3))/5(3-a)=(a-3)(b-2)/5(3-a)= =(a-3)(b-2)/5(-1)(a-3)=(2-b)/5
D=(-11)^2-4*2*5=121-40=81; x1=(11-9)/4, x2=(11+9)/4. x1=1/2, x2=5. Ответ: x1=1/2, x2=5.
Пусть х1 и х2 это корни уравнения.
По условию х1/х2=6, отсюда х1 = 6*х2.
По виету х1 + х2 = -2, тогда 6*х2 + х2 = -2, х2 = -2/7, х1=-6*2/7=-12/7
По виету q = x1*x2 = (-2/7)*(-12/7) = 24/49.