Решите на множестве R неравенство:
1)x(x+5)-2>4x
2)(5x+1)(3x-1)>(4x-1)(x+2)
1)
x(x+5)-2>4x
x^2+5x-2-4x>0
x^2+x-2>0
(+) = -1 !-2
(*) = -2 ! 1
(x+2)(x-1)>0
+ -- +
---(-2)-------(1)----->x
x прин. (-беск; -2) V (1;+беск)
2)
(5x+1)(3x-1)>(4x-1)(x+2)
15x^2 -2x -1 -4x^2 -7x+3>0
11x^2 - 9x +2>0
(+) = -9 !11/11=1
(*) = 22 ! 2/11=2/11
11(x-1)(x-2/11)>0
-------(2/11)----------(1)-------->x
x прин. (-беск; 2/11) V (1;+беск)
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Answers & Comments
1)
x(x+5)-2>4x
x^2+5x-2-4x>0
x^2+x-2>0
(+) = -1 !-2
(*) = -2 ! 1
(x+2)(x-1)>0
+ -- +
---(-2)-------(1)----->x
x прин. (-беск; -2) V (1;+беск)
2)
(5x+1)(3x-1)>(4x-1)(x+2)
15x^2 -2x -1 -4x^2 -7x+3>0
11x^2 - 9x +2>0
(+) = -9 !11/11=1
(*) = 22 ! 2/11=2/11
11(x-1)(x-2/11)>0
+ -- +
-------(2/11)----------(1)-------->x
x прин. (-беск; 2/11) V (1;+беск)