(х*(х-1)+х*(х+1))/х²-1=8/3
3*(х²-х+х²+х) / 3*(х²-1)=8 *(х²-1) /3*(х²-1)
6х²=8х²-8
2х²-8=0
х²=8:2
х²=4
х₁= 2
х₂= -2
Формула для суммы: Sn=(a1+an)*n/2.
Здесь: а1=5, a20=2+60=62, S=(5+62)*20/2=670.
1/2(cos70-cos90)1/2(cos50-cos90)=1/4cos50cos70
cos90=0
cos70cos50=cos70cos50
5sin^2(x)+8cos(x)=8
8-5sin^2(x)-8cos(x)=0
2.5-5sin^2(x)+5.5-8cos(x)=0
5cos^2(x)+3-8cos(x)=0
cos(x)=(8+-sqrt(64-60))/10=(8+-2)/10= 1 или 0,6
Значит:
x = 2 π n, n ∈ <span>Z
</span>x = 2 π k - arccos(3/5), k ∈<span> Z
</span>x = 2 π k + arccos(3/5), k ∈<span> Z
Но sin(x)>0
Тогда:
</span>x = 2 π k + arccos(3/5), k ∈ Z