Решите неравенство ((x^2-12x+10)/(x-1))+((x^2-15x+5)/(x-5))= - вопрос №434692721210121555211 от katyasergienko2004 13.04.2022 07:37

Question

Математика: Решите неравенство ((x^2-12x+10)/(x-1))+((x^2-15x+5)/(x-5))= 2x-11

katyasergienko2004 · Answer

(x^2-12x+10)/(x-1) + (x^2-15x+5)/(x-5) ≤ 2x-11 <=>
<=> [(x^2-12x+10)(x-5) + (x^2-15x+5)(x-1) - (2x-11)(x-1)(x-5)] / [(x-1)(x-5)] ≤ 0

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(x^2-12x+10)(x-5) - (2x-11)(x-1)(x-5) =
= (x^2-12x+10-2x^2+13x-11)(x-5) =
= (-x^2+x-1)(x-5) =
= -x^3+x^2-x+5x^2-5x+5 =
= -x^3+6x^2-6x+5

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(x^2-15x+5)(x-1) =
= x^3-15x^2+5x-x^2+15x-5 =
= x^3-16x^2+20x-5

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-x^3+6x^2-6x+5+x^3-16x^2+20x-5 =
= -10x^2+14x

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-2x(5x-7) / [(x-1)(x-5)] ≤ 0 <=>
<=> 2x(5x-7) / [(x-1)(x-5)] ≥ 0

x≠1; x≠5

_+_[0]_-_(1)_+_[1.4]_-_(5)_+_

ответ:
(-∞;0] ∨ (1;1.4] ∨ (5;+∞)

Решите неравенство ((x^2-12x+10)/(x-1))+((x^2-15x+5)/(x-5))=< 2x-11