(4х + 3)(х-1) - (3х - 2)(х+2) = 10 - 5х
4х * х + 4х * (-1) + 3*х +3*(-1) - (3х*х + 3х*2 - 2*х -2*2) = 10 - 5х
4х² - 4х + 3х - 3 - (3х² + 6х - 2х - 4) = 10 - 5х
4х² - х - 3 - 3х² - 4х + 4 = 10 - 5х
х² - 5х + 1 = 10 - 5х
х² - 5х + 1 - 10 + 5х = 0
х² - 9 = 0
х² - 3² = 0
(х - 3)(х +3) = 0
х - 3= 0
х₁ = 3
х + 3 = 0
х₂ = - 3
Y = (2x+5)/3 = 2x/3 + 5/3
Это растущая прямая, разрывов нет.
y(-1) = -2/3 + 5/3 = 3/3 = 1
y(5) = 10/3 + 5/3 = 15/3 = 5
y ∈ [1; 5]
1
sinx=1/2
x=(-1)^n*π/6+πn,n∈z
2
перейдем к основанию 2
(log(2)3+5):1/(log(2)3-1) -(log(2)3+3):1/(log(2)3+1)=
=(log(2)3+5)*(log(2)3-1) -(log(2)3+3)*(log(2)3+1)=
=log²(2)(3)-log(2)3+5log(2)3-5-log²(2)3-log(2)3-3log(2)3-3=-8
3
sina-cosa=0,5
sinacosa=[1-(sina-cosa)²]:2=(1-0,25):2=0,75:2=0,375
sin³a-cos³a=(sina-cosa)(sin²a+sinacosa+cos²a)=0,5*(1+0,375)=0,6875
4
log(32)log(2)(2^1/16)=log(3)(1/16)=-4/5=-0,8
5
sina-cosa=-0,25
sinacosa=[1-(sina-cosa)²]:2=(1-0,0625):2=0,9375:2=0,46875
32(sin³a-cos³a)=32(sina-cosa)(sin²a+sinacosa+cos²a)=
=32*(-0,25)*(1+0,46875)=-11,75
6
log(√a)9=2
2log(a)3/(0,5)=6log(a)3
6log(a)3=2
log(a)3=1/3
log(a)27=3log(a)3=3*1/3=1
7
t^(17/3):t^(8/3)=t^(17/3-8/3)=t²
8
-ctgx=√3
ctgx=-√3
x=5π/6+πn,n∈z