Lg(3x-11)+lg(x-27)=3 ОДЗ: 3х-11>0 и х-27>0
lg(3x-11)(x-27)=lg1000 3x>11 x>27
(3x-11)(x-27)=1000 x>3 2/3
3x²-11x-81x+297-1000=0 <u> x>27</u>
3x²-92x-703=0
D=(-92)²-4*3(-703)=16900=130²
x1=6 1/3<27 x2=37
Ответ: 37
1) √3ctg(3π/2 - x) = - √3
tgx = - 1
x = - π/4 + πk, k∈Z
2) 1 - 2*sin^2(π/2 - x) = 0
cos^2x = 1/2
a) cosx = - √2/2
x = (+ -)arccos(- √2/2) + 2πn, n∈Z
x = (+ -)*(π - arccos(√2/2) + 2πn, n∈Z
x = (+ -)*(π - π/4) + 2πn, n∈Z
x1 = (+ -)*( 3π/4) + 2πn, n∈Z
b) cos^2x = √2/2
x = (+ -)arccos(√2/2) + 2πn, n∈Z
x2 = (+ -)*( π/4) + 2πn, n∈Z
3) ctg(3π/2 + x)*ctg(x - π/2) = 1
tgx*tgx = 1
tg^2x = 1
a) tgx = - 1
x = - π/4 + πk, k∈Z
b) tgx = 1
x = π/4 + πn, n∈Z
1) (m+1)x-4<(1-3m)x+2
mx+x-4<x-3xm+2
mx-4<-3xm+2
4xm<6
x<6/4m
x<3/2m
2) (2+m)x+6<(2-3m)x-1
2x+mx+6<2x-3mx-1
mx+6<-3mx-1
4mx<-7
x>-7/4m