Решение
1 + cos(x + π/2) + cos(x - π/2) =
= 1 - sinx - sinx = 1 - 2sinx
при x = 5π/12
1 - 2sinx = 1 - 2sin(5π/12) = 1 - 2sin75° = 1 - 2 * 0,9659 = 1 - 1,9318 = - 0,9318
ОДЗ
{(x+3)/(x-3)>0⇒x<-3 U x>3
{x-3>0⇒x>3
{x+3>0⇒x>-3
x∈(3;∞)
перейдем к основанию 2
log(2)4/log(2)[(x+3)/(x-3)]=2(log(2)(x-3)/log(2)(1/2)-log(2)√(x+3)/log(2)(1/√2))
2/log(2)[(x+3)/(x-3)]=2(-log(2)(x-3)-1/2log(2)(x+3)/(-1/2))
2/log(2)[(x+3)/(x-3)]=2(log(2)[(x+3)/(x-3)]
log(2)[(x+3)/(x-3)]=t
2/t=2t
2t²=2
t²=1
t1=-1 U t2=1
log(2)[(x+3)/(x-3)]=-1
(x+3)/(x-3)=1/2⇒2x+6=x-3⇒x=-9∉ОДЗ
log(2)[(x+3)/(x-3)]=1
(x+3)/(x-3)=2⇒x+3=2x-6⇒x=9
Ответ х=9
преобразуем показатель степени по формуле
Х²+у²-8х+2у+17=0
(х²-8х+16)+(у²+2у+1)=0
(х-4)²+(у+1)²=0
(х-4)²>0;(у+1)²>0
х-4=0;х=4
у+1=0;у=-1
ответ х=4;у=-1