Question

помогите решить уравнение

Answer 1

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

Answer 2

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
$frac{x-5}{x+1} = frac{ x^{2} +4-5x}{ x^{2} -4-3x} -1 \ frac{x-5}{x+1} = frac{ (x-4)(x-1)}{ (x-4)(x+1)} -1 \ frac{x-5}{x+1} = frac{x-1}{x+1} -1 \ frac{x-1}{x+1} - frac{x+1}{x+1} - frac{x-5}{x+1} =0 \ frac{x-1-x-1-x+5}{x+1} =0 \ frac{-x+3}{x+1} =0 \ -x+3=0 \ x=3$