Question

tìm GTNN

3x^2-8x-2

 

Answer 1

Đặt \(A=3\left(x^2-\dfrac{8}{3}x\right)-2=3\left(x^2-2.\dfrac{4}{3}x+\dfrac{16}{9}-\dfrac{16}{9}\right)-2\)

\(=3\left(x^2-2.\dfrac{4}{3}x+\dfrac{16}{9}\right)-\dfrac{16}{3}-2\)

\(=3\left(x-\dfrac{4}{3}\right)^2-\dfrac{22}{3}\ge-\dfrac{22}{3}\)

\(A_{min}=-\dfrac{22}{3}\) khi \(x=\dfrac{4}{3}\)

Answer 2

Ta có: \(3x^2-8x-2\)

\(=3\left(x^2-\dfrac{8}{3}x-\dfrac{2}{3}\right)\)

\(=3\left(x^2-2\cdot x\cdot\dfrac{4}{3}+\dfrac{16}{9}-\dfrac{22}{9}\right)\)

\(=3\left(x-\dfrac{4}{3}\right)^2-\dfrac{22}{3}\ge-\dfrac{22}{3}\forall x\)

Dấu '=' xảy ra khi \(x=\dfrac{4}{3}\)