2
sinx+2cos2x=1,5
sinx+2-4sin²x=1,5
sinx=a
4a²-a-0,5=0
D=1+8=9
a1=(1-3)/8=-1/4⇒sinx=-1/4⇒
x=-arcsin1/4+2πk U x=arcsin1/4-π+2πk,k∈z
a2=(1+3)/8=1/2⇒sinx=1/2⇒
x=π/6+2πk U x=5π/6+2πk,k∈z
4
3*3^(2x²-6x+2)+6^(x²-3x+1)-2*2^(2x²-6x+2)=0/2^(2x²-6x+2)
3*(3/2)^(2x²-6x+2)+(3/2)^(x²-3x+1 -2=0
(3/2)^(x²-3x+1)=a
3a²+a-2=0
D=1+24=25
a1=(-1-5)/6=-1⇒(3/2)^(x²-3x+1)=-1 нет решения
a2=(-1+5)/6=2/3⇒(3/2)^(x²-3x+1)=2/3⇒x²-3x+1=-1
x²-3x+2=0
x1+x2=3 u x1*x2=2
x1=1 U x2=2
5
3^x*(3+9+27)>4^x*(1+4)
39*3^x>5*4^x
(3/4)^x>5/39
x7
{x²+5x+4≥0 x1+x2=-5 U x1*x2=4 x1=-4 U x2=-1⇒x≤-4 U x≥-1
{x²+5x+4>(x+2)²⇒x²+5x+4>x²+4x+4⇒x>0
x∈(0;∞)