помогите решить уравнение. Created by kasatka09. algebra-ru

помогите решить уравнение...

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X²-5x+4=(x-1)(x-4)
x1+x2=5 U x1*x2=4⇒x1=1 U x2=4
x²-3x-4=(x+1)(x-4)
x1+x2=3 U x1*x2=-4⇒x1=-1 U x2=4
(x-5)/(x+1)=(x-1)(x-4)/[(x+1)(x-4)]-1
ОДЗ х≠-1 и х≠4
(x-5)/(x+1)=(x-1)/(x+1)-1
x-5=x-1-x-1
x=-2+5
x=3

1 votes Thanks 1

Emmie1

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По теореме Виета
x1*x2=4
x1+x2= 5
x1=4; x2=1
x^2+4-5x=(x-4)(x-1)
По теореме Виета
x1*x2=-4
x1+x2= 3
x1=4; x2=-1
x^2-4-3x=(x-4)(x+1)
ОДЗ: x≠4; x≠-1
$\frac{x-5}{x+1} = \frac{ x^{2} +4-5x}{ x^{2} -4-3x} -1 \\ \frac{x-5}{x+1} = \frac{ (x-4)(x-1)}{ (x-4)(x+1)} -1 \\
 \frac{x-5}{x+1} = \frac{x-1}{x+1} -1 \\ \frac{x-1}{x+1} - \frac{x+1}{x+1} - \frac{x-5}{x+1} =0 \\ \frac{x-1-x-1-x+5}{x+1} =0 \\ \frac{-x+3}{x+1} =0 \\ -x+3=0 \\ x=3$

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