1) (х⁴+4х²-5)/ (x²+5x+6) ≤ 0
x²=a
4a²+a-3=0
D=1+48=49
a1=(-1-7)/8=-1 ⇒x²=-1 U a2=(-1+7)/8=0,75⇒x²=3/4⇒x=-√3/2 U x=√3/2
x1+x2=-5 U x1*x2=6⇒x1=-3 U x2=-2
+ _ + _ +
(-3)(-2)[-√3/2][√3/2]
x∈(-3;-2) U [-√3/2;√3/2]
2)(x⁴-2x²-8)/ (x⁴-2x²-3) > 0
x²=a
a²-2a-8=0
a1=a2=2 U a1*a2=-8
a1=-2⇒x²=-2 U a2=4⇒x²=4⇒x=-2 U x=2
x²=b
b²-2b-3=0
b1=b2=2 U b1*b2=-3
b1=-1⇒x²=-1 U b2=3⇒x=-√3 U x=√3
+ _ + _ +
(-2)(-√3)(√3)(2)
x∈(-∞;-2) U (-√3;√3) U (2;∞)
1) (х⁴+4х²-5)/ (x²+5x+6) ≤ 0
x²=a
4a²+a-3=0
D=1+48=49
a1=(-1-7)/8=-1 ⇒x²=-1 U a2=(-1+7)/8=0,75⇒x²=3/4⇒x=-√3/2 U x=√3/2
x1+x2=-5 U x1*x2=6⇒x1=-3 U x2=-2
+ _ + _ +
(-3)(-2)[-√3/2][√3/2]
x∈(-3;-2) U [-√3/2;√3/2]
2)(x⁴-2x²-8)/ (x⁴-2x²-3) > 0
x²=a
a²-2a-8=0
a1=a2=2 U a1*a2=-8
a1=-2⇒x²=-2 U a2=4⇒x²=4⇒x=-2 U x=2
x²=b
b²-2b-3=0
b1=b2=2 U b1*b2=-3
b1=-1⇒x²=-1 U b2=3⇒x=-√3 U x=√3
+ _ + _ +
(-2)(-√3)(√3)(2)
x∈(-∞;-2) U (-√3;√3) U (2;∞)
б)2(x-1)^2
в)-5(a-b)^2
г)-3x(2x+1)^2
а)9x^2+21x-9x^2+6x-1=27x-1
б)y^2-9-y^2+2y-1=2y-10
в)4ab-b^2+2a^2-4ab+2b^2=2a^2
г)c^2-6c+5-c^2+12c-36=6c-36