Question

Tìm GTNN của 2x^2-2x+4

Answer 1

2x²-2x+4

=2(x²-x+2)

=2(x²-x+\(\frac{1}{4}+\frac{7}{4}\))

=2(x-\(\frac{1}{2}\))²+\(\frac{7}{2}\)

Ta có 2(x-\(\frac{1}{2}\))²+\(\frac{7}{2}\) ≥ \(\frac{7}{2}\) ∀x

Dấu "=" xảy ra

⇔(x-\(\frac{1}{2}\))²=0

⇔x-\(\frac{1}{2}\)=0

⇔x=\(\frac{1}{2}\)

Vậy...

Answer 2

2x²-2x+4

=x²-x+2

=x²-x+\(\frac{1}{4}+\frac{7}{4}\)

=(x+\(\frac{1}{2}\))²+\(\frac{7}{4}\) ≥ \(\frac{7}{4}\) ∀x

Dấu bằng xảy ra

⇔ x+\(\frac{1}{2}\)=0

⇔ x=-\(\frac{1}{2}\)

Vậy...