`#tnvt`
`(x+1)(x+2)(x+3)(x+4)`
`=(x+1)(x+4)(x+2)(x+3)`
`=(x^2+5x+4)(x^2+5x+6)`
Đặt `x^2+5x+5=a`
`=(a-1)(a+1)`
`=a^2-1`
Vì `a^2>=0<=>a^2-1>=-1`
Dấu `=` xảy ra khi `a=0<=>x^2+5x+5=0`
`<=>x^2+2.x. 5/2+25/4-5/4=0`
`<=>(x+5/2)^2-5/4=0`
`<=>(x+5/2-\frac{\sqrt{5}}{2})(x+5/2+\frac{\sqrt{5}}{2})=0`
`<=>[(x=\frac{\sqrt{5}-5}{2}),(x=\frac{-\sqrt{5}-5}{2}):}`
Vậy `GTNNNN=-1` khi `x=\frac{+-\sqrt{5}-5}{2}`
