Решите уравнения! 2sin^2 x/2-3 sin x/2+1=0 3tg^2+2tgx-1=0

1) sin(x/2)=t⇒2t^2-3t+1=0⇒t1=(3+√9-8)/4=(3+1)/4=1; t2=(3-√9-8)/4=(3-1)/4=1/2 sin(x/2)=1⇒x/2=π/2+2πn⇒x=π+4πn sin(x/2)=1/2⇒x/2=(-1)^n*π/6+πn⇒x=(-1)^n*π/3+2πn 2) 3tg^2+2tgx-1=0tgx=t⇒3t^2+2t-1=0⇒t1=(-1+√1+3)/3=1/3; t2=(-1-√1+3)/3=-1tgx=1/3⇒x=arctg(1/3)+πntgx=-1⇒x=-π/4+πn

{а1+11d=6

{a1+23d=12

 

{a1=6-11d

{6-11d+23d=12

12d=12-6

12d=6

d=6: 12

d=0,5

 

a1=6-11d=6-11*0,5=6-5,5=0,5

 

a18=a1+17d=0,5+17*0,5=9