Решение во вложении.Первая часть
Вариант 4
152/(x-1)-54=-5x;
(152-54(x-1)+5x(x-1))/(x-1)=0
(5x^2-49x+98)/(x-1)=0 <=>
5x^2-49x+98=0 и x-1<>0
5x^2-49x+98=0
D= 49*49-4*5*98= 2401-1960=441
x= (49+/- 21)/10
x1=14/5
x2=7
Проверка: Если x=7, то x-1<>0
Если x=14/5, то x-1<>0
Ответ: 7, 14/5.
2 1/2 х 2/15 - 3 5/6 +1/4 = -3 1/4
1) 2 1/2 х 2/15 = 5/2 х 2/15 = 1/3
2) 1/3 -3 5/6 = -3 -5/6 +1/3 = -3 - 3/6 = -3 -1/2 = -3 1/2
3) -3 1/2 + 1/4 = -3 +1/4 -1/2 = -3 -1/4 = -3 1/4
1)
10sin²(x)+11sin(x)-8=0
sin(x)=t, |t|≤1
10t²+11t-8=0
D=121+320=441=21²
t1=(-11+21)/20=1/2
t2=-(11-21)/20=-1.6∉|t|≤1
sin(x)=1/2
x=(-1)^n *arcsin(1/2)+πn,n∈Z
<em><u>x=(-1)^n *π/6 +πn, n∈Z</u></em>
2)
4sin²(x)-11cos(x)-11=0
4(1-cos²(x))-11cos(x)-11=0
4-4cos²(x)-11cos(x)-11=0
4cos²(x)+11cos(x)+7=0
cosx=t, |t|≤1
4t²+11t+7=0
D=121-112=9=3²
t1=(-11+3)/8=-1
t2=(-11-3)/8=-7/4∉|t|≤1
cos(x)=-1
<em><u>x=π+2πn,n∈Z</u></em>
3)
4sin²(x)+9sin(x)cos(x)+2cos²(x)=0 |:(cos²(x)≠0)
4tg²(x)+9tg(x)+2=0
tg(x)=t
4t²+9t+2=0
D=81-32=49=7²
t1=(-9+7)/8=-1/4
t2=(-9-7)/8=-2
tg(x)=-1/4
x=arctg(-1/4)+πn,n∈Z
<em><u>x=-arctg1/4+πn,n∈Z</u></em>
tg(x)=-2
x=arctg(-2)+πm,m∈Z
<em><u>x=-arctg2+πm,m∈Z</u></em>
4)
3tg(x)-8ctg(x)+10=0
3tg(x)-8(1/tg(x))+10=0 |*tg(x)≠0
3tg²(x)+10tg(x)-8=0
tg(x)=t
3t²+10t-8=0
D=100+96=196=14²
t1=(-10+14)/6=2/3
t2=(-10-14)/6=-4
tg(x)=2/3
<em><u>x=arctg(2/3)+πn,n∈Z</u></em>
tg(x)=-4
x=arctg(-4)+πm,m∈Z
<em><u>x=-arctg4+πm,m∈Z</u></em>
5)
3sin(2x)+8sin²(x)-7*1=0
6sin(x)cos(x)+8sin²(x)-7(cos²(x)+sin²(x))=0 |:cos²x≠0
6tg(x)+8tg²(x)-7-7tg²(x)=0
tg²(x)+6tg(x)-7=0
tg(x)=t
t²+6t-7=0
D=36+28=64=8²
t1=(-6+8)/2=1
t2=(-6-8)/2=-7
tg(x)=1
x=arctg(1)+πn,n∈Z
<em><u>x=π/4 +πn,n∈Z</u></em>
tg(x)=-7
x=arctg(-7)+πm,m∈Z
<em><u>x=-arctg7+πm,m∈Z</u></em>
-12x+12x-12-12x-6=-12x-12-6
-12x=-18
x=-1,5
