Question

Решите неравенства 1) (х -5)(х-1,5) < 0 2) 0,4х (7-х)(х-0,8)《 0 《- больше либо равно

Answer 1

1) (x-5)(x-1.5)∠0
x²-1.5x-5x+7.5∠0
x²-6.5x+7.5∠0
a=1 b=-6.5 c=7.5
x1/2=(-b+-√(b²-4ac))/2a
x1/2=(6.5+-√(42.25-30))/2=(6.5+-√12.25)/2=(6.5+-3.5)/2
x1=(6.5-3.5)/2=3/2
x1=1.5
x2=(6.5+3.5)/2=10/2
x2=5

2) 0.4(7-x)(x-0.8)≤0
0.4(7x-5.6-x²+0.8x)≤0
0.4(-x²+7.8x-5.6)≤0
-0.4x²+3.12x-2.24≤0
-0.4x²+3.12x-2.24≤0
a=-0.4 b=3.12 c=-2.24
x1/2=(-b+-√(b²-4ac))/2a 
x1/2=(-3.12+-√(9.7344-3.584))/(-0.8)=(-3.12+-√6.1504)/(-0.8)
x1/2=(-3.12+-2.48)/(-0.8)
x1=(-3.12-2.48)/(-0.8)=-5.6/(-0.8)
x1=7
x2=(-3.12+2.48)/(-0.8)=-0.64/(-0.8)
x2=0.8
x1≤7 x2≤0.8