Question

Tìm GTNN của BT

1.D=x^2-x-1

2.H=9x^2-36x-136

3.I=x(x-5)

Answer 1

a)D=x²-x-1

\(=\left(x-\frac{1}{2}\right)^2-\frac{5}{4}\)

Ta thấy:\(\left(x-\frac{1}{2}\right)^2-\frac{5}{4}\ge0-\frac{5}{4}=-\frac{5}{4}\)

\(\Rightarrow D\ge-\frac{5}{4}\)

Dấu = khi x=1/2

Vậy Dmin=-5/4 <=>x=1/2

b)H=9x²-36x-136

\(=9\left(x-2\right)^2-172\)

Ta thấy:\(9\left(x-2\right)^2-172\ge0-172=-172\)

\(\Rightarrow H\ge-172\)

Dấu = khi x=2

Vậy Dmin=-172 <=> x=2

c)I=x(x-5)

\(=\frac{1}{4}\left(2x-5\right)^2-\frac{25}{4}\)

Ta thấy:\(\frac{1}{4}\left(2x-5\right)^2-\frac{25}{4}\ge0-\frac{25}{4}=-\frac{25}{4}\)

\(\Rightarrow I\ge-\frac{25}{4}\)

Dấu = khi x=5/2

Vậy Imin=-25/4 <=>x=5/2