Question

[Nguyễn Khoa]

Các bạn giúp mình bài này nhé! Mình cảm ơn! :D

Answer 1

[Nguyễn Lê Phước Thịnh]

4: \(D=x^2-2\cdot x\cdot\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{3}{4}\)

\(=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\forall x\)

Dấu '=' xảy ra khi \(x=\dfrac{1}{2}\)

Answer 2

[Nguyễn Hoàng Minh]

\(A=\left(x^2-6x+9\right)-7=\left(x-3\right)^2-7\ge7\\ A_{min}=7\Leftrightarrow x=3\\ B=\left(9x^2+6x+1\right)-4=\left(3x+1\right)^2-4\ge-4\\ B_{min}=-4\Leftrightarrow x=-\dfrac{1}{3}\\ C=\left(x^2-2\cdot\dfrac{5}{2}x+\dfrac{25}{4}\right)-\dfrac{9}{4}=\left(x-\dfrac{5}{2}\right)^2-\dfrac{9}{4}\ge-\dfrac{9}{4}\\ C_{min}=-\dfrac{9}{4}\Leftrightarrow x=\dfrac{5}{2}\\ D=\left(x^2-x+\dfrac{1}{4}\right)+\dfrac{3}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\\ D_{min}=\dfrac{3}{4}\Leftrightarrow x=\dfrac{1}{2}\)

\(E=3\left(x^2+2\cdot\dfrac{1}{3}x+\dfrac{1}{9}\right)-\dfrac{4}{3}=3\left(x+\dfrac{1}{3}\right)^2-\dfrac{4}{3}\ge-\dfrac{4}{3}\\ E_{min}=-\dfrac{4}{3}\Leftrightarrow x=-\dfrac{1}{3}\\ F=x^2-2x+1+x^2-4x+4+2021\\ F=2\left(x^2-3x+\dfrac{9}{4}\right)+\dfrac{4031}{2}=2\left(x-\dfrac{3}{2}\right)^2+\dfrac{4031}{2}\ge\dfrac{4031}{2}\\ F_{min}=\dfrac{4031}{2}\Leftrightarrow x=\dfrac{3}{2}\)