Question

Tìm GTNN của \(x^4-6x^3+10x^2-6x+9\)

Answer 1

`A=x^4 -6x^3 +10x^2 -6x +9`

`=x^4 -6x^3 +9x^2  +x^2 -6x+9`

`=x^2 (x^2 -6x+9)+(x^2 -6x+9)`

`=x^2 (x-3)^2 +(x-3)^2`

`=[x(x-3)]^2+(x-3)^2`

Dấu "=" xảy ra `<=>{(x(x-3)=0),(x-3=0):}`

`<=>x-3=0`

`<=>x=3`

Vậy `A_(min) =0<=>x=3`