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Truyen Nguyen
1 tuần trước

giải phương trình x(x+2)(x+4)(x+6)=105

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Kaitokid208
1 tuần trước

!

x(x+2)(x+4)(x 

<=> [ x(x + 6)][ (x + 2)(x + 4)] =105

<=> (x^2 + 6x)(x^2 + 6x + 8) = 105

Đặt a = x^2 + 6x + 4

=> (a - 4)(a + 4) = 105

<=> a^2 - 16 = 105

<=> a^2 = 121

<=> a = \pm 11

Với a = 11

=> x^2 + 6x + 4 = 11

<=> x^2 + 6x - 7 = 0

<=> (x + 7)(x - 1) = 0

<=> x = -7 hoặc x = 1

Với a = -11

=> x^2 + 6x + 4 = -11

<=> x^2 + 6x + 15 = 0

<=> x^2 + 6x + 9 + 6 = 0

<=> (x + 3)^2 + 6 = 0 (Vô lí)

Vậy S = {-7 ; 1}

 

Ác Quỷ
1 tuần trước

x(x+2)(x+4)(x+6)=105

Ta có: 105=1.3.5.7=1.(1+2).(1+4).(1+6)

Vậy x=1

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