Question

Tìm x biết : x( x + 1 )( x + 2 )( x + 3 ) = 24 

Answer 1

\(\Rightarrow x\left(x+3\right)\left(x+1\right)\left(x+2\right)=24\)

\(\Rightarrow\left(x^2+3x\right)\left(x^2+3x+2\right)=24\)

Đặt \(x^2+3x+1=t\)

\(\Rightarrow\left(t-1\right)\left(t+1\right)=24\)

\(\Rightarrow t^2-1=24\Rightarrow t^2=25\Rightarrow t=5;-5\)

Xét t=5 thì \(x^2+3x+1=5\Rightarrow x^2+3x-4=0\)

\(\Rightarrow x^2-x+4x-4=0\)

\(\Rightarrow x\left(x-1\right)+4\left(x-1\right)=0\)

\(\Rightarrow\left(x+4\right)\left(x-1\right)=0\Rightarrow x=-4;1\)

Xét t=-5 ta có

\(x^2+3x+1=-5\Rightarrow x^2+3x+6=0\)

\(\Rightarrow x_1=\frac{-3+\sqrt{15}i}{2};x_2=\frac{-3-\sqrt{15}i}{2}\)

mà \(x\in Z\)nên x=-4;1