27^(1/2)=(3^(3))^(1/2)=3^(3/2)
(1/9)^(3/4)=(3^(-2))^(3/4)=3^(-6/4)=3^(-3/2)
27^(1/2)*(1/9)^(3/4)=3^(3/2)*3^(-3/2)=3^(0)=1
(27^(1/2)**(1/9)^(3/4))^(4/3)= [b]1^(4/3)=1[/b]
2.
2lg5+(1/2)lg16=lg5^2+lg16^(1/2)=lg25+lg4=lg(25*4)=lg100=2
[b]2lg5+(1/2)lg16=2[/b]
3.
tg(π/3)=sqrt(3)
tg^2(π/3)=3
cos(3π/4)=-sqrt(2)/2
cos^2(3π/4)=1/2
[b]tg^2(π/3)- cos^2(3π/4)=3-(1/2)=2,5[/b]
4.
ОДЗ: -x > 0 ⇒ x <0
Возводим в квадрат
20-х=(-x)^2
x^2+x-20=0
D=1-4*(-20)=81
x_(1)=(1-9)/2=-4; x_(2)=(1+9)/2=5
x=5 не является корнем, не удовл ОДЗ
О т в е т. [b]-4[/b]
5.
(1/5)^(3-x)=25^(1-2x)
(5^(-1))^(3-x)=(5^(2))^(1-2x)
5^(x-3)=5^(2-4x)
x-3=2-4x
x+4x=2+3
5x=5
[b]x=1[/b]
6.