Question

6.tim gia tri nho nhat cua bieu thuc.

D=2x^2-6x

Answer 1

Answer 2

D= 2x² - 6x

  = 2(x² - 3x +\(\dfrac{9}{4}\)) - \(\dfrac{9}{2}\)

  = 2[x² - 2.x.\(\dfrac{3}{2}\) + (\(\dfrac{3}{2}\))² ] - \(\dfrac{9}{2}\)

  = 2 (x - \(\dfrac{3}{2}\))² - \(\dfrac{9}{2}\)

Ta có: 

2(x - \(\dfrac{3}{2}\))² ≥ 0 ⇒ 2 (x - \(\dfrac{3}{2}\))² - \(\dfrac{9}{2}\) ≥ -\(\dfrac{9}{2}\)

Hay D≥ -\(\dfrac{9}{2}\)

Dấu = xảy ra ⇔ (x - \(\dfrac{3}{2}\)) = 0 ⇔ x = \(^{\dfrac{3}{2}}\)

Vậy Min_D = - \(\dfrac{9}{2}\) ⇔ x = \(\dfrac{3}{2}\)