Bất cẩn quá :<< Xl nhaa =)) Sửa câu b ạ :
\(B=\left(x-2\right)\left(x-5\right)\left(x^2-7x-10\right)=\left(x^2-7x+10\right)\left(x^2-7x-10\right)=\left(x^2-7x\right)^2-100\)
\(\left(x^2-7x\right)^2\ge0\Rightarrow\left(x^2-7x\right)^2-100\ge-100\Rightarrow B\ge-100\)
=> B min = -100
\(\Leftrightarrow\left(x^2-7x\right)^2=0\)
\(\Leftrightarrow x\left(x-7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=7\end{matrix}\right.\)
Vậy .....................
DƯƠNG PHAN KHÁNH DƯƠNG Dư lày đúng không nhỉ ??
a) \(A=x^2-x+1=\left(x^2-2.x.\dfrac{1}{2}+\dfrac{1}{4}\right)+\dfrac{3}{4}=\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\)
Có : \(\left(x-\dfrac{1}{2}\right)^2\ge0\Rightarrow\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\ge\dfrac{3}{4}\)
\(\Rightarrow\) A min = \(\dfrac{3}{4}\)
\(\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2=0\Leftrightarrow x=\dfrac{1}{2}\)
Vậy ................... (tự kết luận)
b) \(B=\left(x-2\right)\left(x-5\right)\left(x^2-7x-10\right)=\left(x^2-7x-10\right)\left(x^2-7x-10\right)=\left(x^2-7x-10\right)^2\ge0\)
=> B min = 0
\(\Leftrightarrow x^2-7x-10=0\)
\(\Leftrightarrow\left(x-2\right)\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=5\end{matrix}\right.\)
Vậy ..................... (tự kết luận)
