Прикрепила фото
Объяснение:
Объяснение:
Sinx+cosx=1-sin2x (1)
sinx+cosx=cos²x+sin²x-2sinxcosx
sinx+cosx=(cosx-sinx)²
sinx+cosx=a
(sinx+cosx)²=a²
sin²x+cos²x+2sinxcosx=1+2sinxcosx⇒2sinxcosx=a²-1
возвращаемся в (1)
1-(a²-1)-a=0
1-a²+1-a=0
a²+a-2=0
применим теорему Виета x²+px+q=0⇒x1+x2=-p U x1*x2=q
a1+a2=-1 U a1*a2=-2
a1=1⇒sinx+cosx=1
sinx+sin(π/2-x)=1
2sinπ/4cos(x-π/4)=1
cos(x-π/4)=1/√2⇒x-π/4=+-π/4+2πn
x=π/4-π/4+2πn,n∈Z⇒x=2πn,n∈Z U x=π/4+π/4+2πn,n∈Z⇒x=π/2+2πn,n∈Z
a2=-2⇒2sinπ/4cos(x-π/4)=-2
cos(x-π/4)=-√2<-1 нет корней
ответ x=π/2+2πn,n∈Z;х=2πn,n∈Z
Подробнее - на -
log(2) 24 - 1/2*log(2) 72 =log(2) 24 - log(2) √72 = log(2) 24 - log(2) √(36*2) = log(2) 24/√(36*2) = log(2) 24/6√2) = log(2) 4/√2 = log(2) 4 - log(2) √2 = 2-1/2 = 3/2
log(3) 18 - 1/3log(3) 72 =log(3) 18 - log(3) ∛72 = log(3) 18 - log(3) ∛(8*9) = log(3) 18/∛(2³*9) = log(3) 18/2∛9 = log(3) 9/∛9 = log(3)9 - log(3) ∛9 = 3 - 2/3 = 6/3 - 2/3 = 4/3
3/2 : 4/3 = 3/2 * 3/4 = 9/8
Iog(2)24-½log(2)72 9
_______________ = -----
Iog(3)18-⅓log(3)72 8