1) (2*х²-4*х)/(х-4)≤0 ОДЗ х-4≠0 х≠4
{2*x²-4*x≤0 {2*x*(x-2)≤0 x1=0 x2=2 x∈(-∞; 0]∪[2; +∞)
{x-4>0 {x>4 x∈(4; +∞)
///////////////0............2//////////////////////////
4\\\\\\\\\\\\\\\\\\\
х∈(4; +∞)
{2*x²-4*x≥0 x∈[0; 2]
{x-4<0 x∈(-∞; 4)<br>.................0////////2.......................
\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\4
х∈[0; 2]
Ответ: х∈[0; 2]∪(4; +∞)
2. 3^(x+1)-84=-3^(x-2)
3*3^(x)+(1/9)*3^(x)=84
Пусть 3^(x)=t
3*t+t/9=84 (*9)
27*t+t=756
28*t=756
t=27
3^(x)=27
3^(x)=3³ так как основания равны, равны и степени.
х=3
Ответ: х=3