Question

Tìm gtnn của A_(x) =(x-1)(x-3)(x-4)(x-6)+ 10

Answer 1

\(A=\left(x-1\right)\left(x-3\right)\left(x-4\right)\left(x-6\right)+10\)

\(A=\left[\left(x-1\right)\left(x-6\right)\right]\left[\left(x-3\right)\left(x-4\right)\right]+10\)

\(A=\left(x^2-7x+6\right)\left(x^2-7x+12\right)+10\)

Đặt \(m=x^2-7x+9\)ta có :

\(A=\left(m-3\right)\left(m+3\right)+10\)

\(A=m^2-3^2+10\)

\(A=m^2+1\)

Thay \(m=x^2-7x+9\)ta có :

\(A=\left(x^2-7x+9\right)^2+1\ge1\forall x\)

Dấu "=" xảy ra \(\Leftrightarrow x^2-7x+9=0\)