Question

(x-4)(x-3)(x-2)(x-1)=24 x(x-3)(x-2)(x-1)=24

Answer 1

1
[(x-4)(x-1)]*[(x-2)(x-3)]=24
(x²-5x+4)*(x²-5x+6)=24
x²-5x+4=a
a(a+2)-24=0
a²+2a-24=0
a1+a2=-2 U a1*a2=-24
a1=-4⇒x²-5x+4=-6
x²-5x+10=0
D=25-40=-15<0 не трешения
a2=4⇒x²-5x+4=4
x²-5x=0
x(x-5)=0
x=0
x=5
2
[x(x-3)]*[(x-2)(x-1)]=24
(x²-3x)*(x²-3x+2)=24
x²-3x=a
a(a+2)=24
a²+2a-24=0
a1+a2=-2 U a1*a2=-24
a1=-4⇒x²-3x=-6
x²-3x+6=0
D=9-24=-15<0 нет решения
a2=4⇔x²-3x=4
x²-3x-4=0
x1+x2=3 U x1*x2=-4
x1=-1 x2=4