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Annaaa117
@Annaaa117
July 2022
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(x-4)(x-3)(x-2)(x-1) =24
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Verified answer
(x-4)(x-3)(x-2)(x-1)=24
(x-4)(x-1) * (x-3)(x-2)=24
(x²-4x-x+4) * (x²-3x-2x+6)=24
(x²-5x+4)(x²-5x+6)=24
Замена переменной:
t=x²-5x
(t+4)(t+6)=24
t²+4t+6t+24=24
t²+10t=24-24
t(t+10)=0
t=0 t+10=0
t= -10
При t=0
x²-5x=0
x(x-5)=0
x=0 x-5=0
x=5
При t= -10
x²-5x= -10
x²-5x+10=0
D=(-5)²-4*10=25-40= -15<0
нет решений
Ответ: 0; 5.
1 votes
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Answers & Comments
Verified answer
(x-4)(x-3)(x-2)(x-1)=24(x-4)(x-1) * (x-3)(x-2)=24
(x²-4x-x+4) * (x²-3x-2x+6)=24
(x²-5x+4)(x²-5x+6)=24
Замена переменной:
t=x²-5x
(t+4)(t+6)=24
t²+4t+6t+24=24
t²+10t=24-24
t(t+10)=0
t=0 t+10=0
t= -10
При t=0
x²-5x=0
x(x-5)=0
x=0 x-5=0
x=5
При t= -10
x²-5x= -10
x²-5x+10=0
D=(-5)²-4*10=25-40= -15<0
нет решений
Ответ: 0; 5.