9.029
1 -
3 > 0 3х-2-х² 7х-4-3х²3х-2-х²=0х²-3х+2=0Д=9-8=1х₁=(3-1)/2=1х₂=4/2=23х-2-х²=-(х-1)(х-2)=(1-х)(х-2)7х-4-3х²=03х²-7х+4=0Д=49-4*3*4=49-48=1х₁=(7-1)/6=1х₂=8/6=4/37х-4-3х²=-3(х-1)(х-4/3)=3(1-х)(х-4/3)
1 -
3 >0 (1-х)(х-2) 3(1-х)(х-4/3)
1 -
1 >0 (1-х)(х-2) (1-х)(х-4/3)
х-4/3 -
х-2 >0 (1-х)(х-2) (1-х)(х-4/3)
2/3 >0 (1-х)(х-2)(х-4/3) 2/3(1-х)(х-2)(х-4/3) >0 х₁=1 х₂=2 х₃=4/3=1 1/3 + - + -------1 ------1 1/3------2--------х∈(-∞; 1) и (4/3; 2)9.031
3х²-10х+3 >0х²-10х+253х²-10х+3=0Д=100-4*3*3=100-36=64х₁=(10-8)/6=2/6=1/3х₂=18/6=33х₂-10х+3=3(х-1/3)(х-3)х²-10х+25=(х-5)²
3(х-1/3)(х-3) >0 (х-5)²3(х-1/3)(х-3)(х-5)(х-5) >0х₁=1/3 х₂=3 х=5 + - + +----- 1/3 ------3--------5-------х∈(-∞; 1/3) и (3; 5) и (5; ∞)9.0345х-20≤х²≤8х{5х-20≤х² {-х²+5х-20≤0 {х²-5х+20≥0{х²≤8х { х(х-8)≤0 {x(x-8)≤0х²-5х+20=0Д=25-80<0 - нет корнейх²-5х+20≥0 при любом хх(х-8)≤0х₁=0 х₂=8 + - +-------0-------8--------х∈[0; 8]Ответ: х∈[0; 8]