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ВНирване
@ВНирване
July 2022
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решить неравенство 1/x^2+8x-9 >= 1/3x^2-5x+2
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sedinalana
Verified answer
X+8x-9=(x+9)(x-1)
x1+x2=-8 U x1*x2=-9⇒x1=-9 U x2=1
3x²-5x+2=3(x-2/3)(x-1)=(3x-2)(x-1)
D=25-24=1
x1=(5-1)/6=2/3 U x2=(5+1)/6=1
--------------------------------------------
1/[(x+9)(x-1)] - 1/[(3x-2)9x-1)]≥0
(3x-2-x-9)/[(x+9)(x-1)(3x-2)]≥0
(2x-11)/[(x+9)(x-1)(3x-2)]≥0
x=5,5 x=-9 x=2/3 x=1
+ _ + _ +
-----------------(9)-----------------(2/3)-----------(1)---------------[5,5]--------------
x∈(-∞;-9 U (2/3;1) U [5,5;∞)
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Verified answer
X+8x-9=(x+9)(x-1)x1+x2=-8 U x1*x2=-9⇒x1=-9 U x2=1
3x²-5x+2=3(x-2/3)(x-1)=(3x-2)(x-1)
D=25-24=1
x1=(5-1)/6=2/3 U x2=(5+1)/6=1
--------------------------------------------
1/[(x+9)(x-1)] - 1/[(3x-2)9x-1)]≥0
(3x-2-x-9)/[(x+9)(x-1)(3x-2)]≥0
(2x-11)/[(x+9)(x-1)(3x-2)]≥0
x=5,5 x=-9 x=2/3 x=1
+ _ + _ +
-----------------(9)-----------------(2/3)-----------(1)---------------[5,5]--------------
x∈(-∞;-9 U (2/3;1) U [5,5;∞)