Question

Tìm GTNN của \(C=\left(x-1\right)\left(x-3\right)\left(x^2-4x+5\right)\)

Answer 1

đặt x²-4x+3=t

⇒x²−4x+5= t+2 pttt:

C= t(t+2)

=t²+2t

=t²+2t +1-1

=(t+1)²-1 ≥-1 (do (t+1)²≥0)

vậy gtnn c=-1 khi t=-1 ⇔ x²-4x+3=-1 ⇔x=2

Answer 2

\(C=\left(x^2-4x+3\right)\left(x^2-4x+5\right)\)

\(C=\left(x^2-4x+3\right)^2+2\left(x^2-4x+3\right)+1-1\)

\(C=\left(x^2-4x+3+1\right)^2-1\)

\(C=\left(x-2\right)^4-1\ge-1\)

\(\Rightarrow C_{min}=-1\) khi \(x=2\)