1)4x²+14x+6=0 D=196-96=100 x1=(-14-10)/8=-3 x2=(-14+10)/8=-0,5 2)x²-4x+3>0 x1+x2=4 U x1*x2=3 x1=1 U x2=3 x∈(-∞;1) U (3;∞) 3)(x-5)(x+5)(x-3)>0 x=-5 x=5 x=3 _ + _ +
-5 3 5 x∈(-5;3) U (5;∞) 4)x^4-5x²+4=0 x²=a a²-5a+4=0 a1+a2=5 U a1*a2=4 a1=1⇒x²=1⇒x=+-1 a2=4 ⇒x²=4⇒x=+-2 (x²-1)(x²-4)/(x²-1)<0 (x-2)(x+2)<0 U x≠+-1 -2<x<2 U x≠+-1 x∈(-2;-1) U (-1;1) U (1;2)
D=196-96=100
x1=(-14-10)/8=-3
x2=(-14+10)/8=-0,5
2)x²-4x+3>0
x1+x2=4 U x1*x2=3
x1=1 U x2=3
x∈(-∞;1) U (3;∞)
3)(x-5)(x+5)(x-3)>0
x=-5 x=5 x=3
_ + _ +
-5 3 5
x∈(-5;3) U (5;∞)
4)x^4-5x²+4=0
x²=a
a²-5a+4=0
a1+a2=5 U a1*a2=4
a1=1⇒x²=1⇒x=+-1
a2=4 ⇒x²=4⇒x=+-2
(x²-1)(x²-4)/(x²-1)<0
(x-2)(x+2)<0 U x≠+-1
-2<x<2 U x≠+-1
x∈(-2;-1) U (-1;1) U (1;2)