1. cos(pi(x-49)/21)=1/2;
pi*(x-49)/21=+-pi/3+2pik;
x-49=+-7+42pik;
x=49+-7+42k
k=-1; x=49+7-42=56-42=14 наименьший полож.кореньx=14.
2. pi*(x-3)/24=t
1+4-4cos^2(t)+8cost=0;
-4cos^2(t) +8cost +5=0;
4cos^2(t)-8cost-5=0;
D=64+80=144=12^2;
cost=(8+12)/8=2,5>1нет решений
или cost=(8-12)/8=-1/2; cos(pi(x-3)/24)=-1/2
pi*(x-3)/24=+-pi/3+2pik;
x-3=+-8+48pik;
x=3+-8+48pik;
k=-1; x=3+8-48=11-48=-37 Наибольший отрицательный корень х=-37
X10 = X1 + 9d = 38 + (-4)*9 = 2
S10= ((38 + 2):2)*10 = 200
<span>2cos²x-1=-1/2
</span><span>2cos²x=1-1/2
</span><span>2cos²x=1/2
</span><span>cos²x=1/4
</span>cos²x-1/4=0
(cosx-1\2)(cosx+1\2)=0
cosx-1\2=0 или cosx+1\2=0
cosx=1\2 cosx=-1\2
x=
+2πn x=2\3π+2πk
36х²+7х+t²=(6x+t)²⇒2·6x·t=7x, t=7/12,
(6x+7/12)²=36x²+7x+49/144.