Question

Tìm giá trị nhỏ nhất của các biểu thức sau: 

a) A = x\(^2\) + 3  

b)  B = (2x + 1)\(^2\) - 5  

c)  C = (2x - 1)\(^{2008}\) + (3y - 2)\(^{2008}\)

Answer 1

Answer 2

a)Ta có: \(x^2\ge0\Rightarrow x^2+3\ge3\)

Dấu "=" xảy ra \(\Leftrightarrow x=0\)

Vậy \(A_{Min}=3 khi x=0\)

b) \(\left(2x+1\right)^2\ge0\Rightarrow\left(2x+1\right)^2-5\ge-5\)

Dấu "=" xảy ra \(\Leftrightarrow x=-\dfrac{1}{2}\)

Vậy \(B_{Min}=-5khix=-\dfrac{1}{2}\)

c) \(\left(2x-1\right)^{2008}\ge0\)

Dấu "=" xảy ra \(\Leftrightarrow x=\dfrac{1}{2}\)

\(\left(3y-2\right)^{2008}\ge0\)

Dấu "=" xảy ra \(\Leftrightarrow y=\dfrac{2}{3}\)

\(\Rightarrow\left(2x-1\right)^{2008}+\left(3y-2\right)^{2008}\ge0\)

Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\\y=\dfrac{2}{3}\end{matrix}\right.\)

Vậy \(C_{Min}=0khix=\dfrac{1}{2}vày=\dfrac{2}{3}\)