√(9-4√5)=√(5 -4√5+4) =√(√5²-4√5 +2²)= √(√5-2)²= √5 - 2
√(7-2√6)= √(6-2√6+1) =√(√6² -2√6+1²)= <span>√(√6-1)</span>²=√6 -1
X=π/3+y
(1+cos2x)/2+(1+cos2y)/2=-3/4
2+cos2x+cos2y=-3/2
cos2x+cos2y=-7/2
2cos(x+y)*cos(x-y)=-7/2
cos(x+y)cos(x-y)=-7/4
cos(2y+π/3)cosπ/3=-7/4
1/2cos(x+y)=-7/4
cos(x+y)=-7/2
нет решения,т.к. -7/2∉[-1;1]
Х - скорость первого
у - скорость второго
L - весь путь
L/(2x)-2=L/(2y)
2(x+y)=L-L/4=3L/4
L/x=t1 - ?
L/y=t2 - ?
******************
t1-4=t2
8(1/t1+1/t2)=3
t1 - ?
t2 - ?
*****************
t1-4=t2
8(t1+t2)=3*t1*t2
8t1+8(t1-4)=3*t1*(t1-4)
16t1-32=3*t1^2-12t1
3*t1^2-28t1+32=0
D=400
t1=8
t2=t1-4=4
4sin2x=7cos²x-<span>7sin²x
</span>
4sin2x=7·(cos²x-<span>sin²x)
</span>4sin2x=7·cos2x
Делим на сos2x≠0
tg2x=7/4
2x=arctg(7/4)+πk, k∈Z<span> <span>
x=(1/2)</span></span>arctg(7/4)+(π/2)·k, k∈Z<span> </span><span>
или
</span><span>7sin²x+4·2sinx·cosx-7cos²x=0
Делим на cos²x≠0
7tg²x+8tgx-7=0
D=64-4·7·(-7)=64+196=260
tgx=(-8-2√65)/14 или tgx=(-8+2√65)/14</span>
tgx=(-4-√65)/7 или tgx=(-4+√65)/7
х=artcg(-4-√65)/7 + πn, n∈Z или х=artcg(-4+√65)/7 + πm, m∈Z