Question

tim GTNN cua bieu thuc A=2x²-10x+11

Answer 1

Ta có :

A = 2x² - 10x + 11

= 2( x² - 2.x.\(\frac{5}{2}\) + \(\frac{25}{4}\) ) - \(\frac{3}{2}\)

= 2(x - \(\frac{5}{2}\))² - \(\frac{3}{2}\)

Ta có :

(x - \(\frac{5}{2}\))^{2 \(\ge0\)}

^<=> 2(x - \(\frac{5}{2}\))^{2 \(\ge0\)}

^<=> 2(x - \(\frac{5}{2}\))² - \(\frac{3}{2}\) \(\ge-\frac{3}{2}\)

Vậy A_min = - \(\frac{3}{2}\) [ Khi (x - \(\frac{5}{2}=0=>x=\frac{5}{2}\))