Решить неравенство : (x² +2x -3) /(x-7)(x+5) < 0
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(x² +2x -3) /(x-7)(x+5) < 0 ;
(x +3)(x-1) /(x-7)(x+5) < 0 * * * a /b < 0 ⇔a *b <0 * * *</span>
(x +3)(x-1)*(x-7)(x+5) < 0 ;</strong>
(x+5)(x +3)(x-1)(x-7) < 0</strong> ; решаем методом интервалов
" +" " - " " +" " -" " +"
----------------(- 5)/////////////////// (- 3) -----------(1) ////////////////////// (7) -------------
ответ : x ∈ ( -5; -3) ∪ (1 ;7) .
* * * * * * * * * * * * * * * * * * * * * *
P.S
x² +2x -3 = x² - x +3x -3 =x(x-1) +3(x-1) =(x-1)(x+3).
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x² +2x -3 = (x -x₁)(x -x₂)
x² +2x -3 =0 D=2² - 4*1(-3) = 4² * * * D/4 =1² -(-3) =4 =2² * * *
x₁ = (-2-4) /2 = -1 -2 = - 3;
x₂ =(-2+4)/2 = -1+2 =1
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