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;∞)
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Verified answer
1) (х⁴+4х²-5)/ (x²+5x+6) ≤ 0x²=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;∞)