1 ОДЗ x(x-2)>0 x=0 x=2 x∈(-∞;0) U (2;∞) lg(x²-2x)=lg(30/10) lg(x²-2x)=lg3 x²-2x=3 x²-2x-3=0 x1+x2=2 U x1*x2=-3 x1=-1 U x2=3 2 log(3)(x²+7x-5)>1 {x²+7x-5>0 (1) {x²+7x-5>3⇒x²+7x-8>0 (2) 1)D=49+20=69 x1=(-7-√69)/2 U x2=(-7+√69)/2 x<(-7-√69)/2 U x>(-7+√69)/2 2)x1+x2=-7 U x1*x2=-8 x1=-8 U x2=1 x<-8 U x>1 x∈(-∞;-8) U (1;∞)
ОДЗ
x(x-2)>0
x=0 x=2
x∈(-∞;0) U (2;∞)
lg(x²-2x)=lg(30/10)
lg(x²-2x)=lg3
x²-2x=3
x²-2x-3=0
x1+x2=2 U x1*x2=-3
x1=-1 U x2=3
2
log(3)(x²+7x-5)>1
{x²+7x-5>0 (1)
{x²+7x-5>3⇒x²+7x-8>0 (2)
1)D=49+20=69
x1=(-7-√69)/2 U x2=(-7+√69)/2
x<(-7-√69)/2 U x>(-7+√69)/2
2)x1+x2=-7 U x1*x2=-8
x1=-8 U x2=1
x<-8 U x>1
x∈(-∞;-8) U (1;∞)