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\(2x^2+10x-1\)
\(=2\left(x^2+5x-\frac{1}{2}\right)\)
\(=2\left(x^2+2.x.\frac{5}{2}+\frac{25}{4}-\frac{27}{4}\right)\)
\(=2\left(\left(x+\frac{5}{2}\right)^2-\frac{27}{4}\right)\)
\(=\frac{-27}{2}-2\left(x+\frac{5}{2}\right)^2\le\frac{-27}{2}\)
\(MinB=\frac{-27}{2}\Leftrightarrow x+\frac{5}{2}=0\Rightarrow x=-\frac{5}{2}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
M=x2+y2-x+6y+10
=(x-1/2)2+(y+3)3+3/4
Ta thấy:(x-1/2)2>=0
(y+3)3>=0
=>(x-1/2)2+(y+3)>=0
=>(x-1/2)2+(y+3)+3/4>=0+3/4=3/4
Dấu "="<=>x=1/2 hoặc y=-3
Vậy...
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![](https://rs.olm.vn/images/avt/0.png?1311)
4.
= x\(^2\)-2.\(\dfrac{5}{2}\)x+\(\dfrac{25}{4}\)-\(\dfrac{13}{4}\)
= (x-\(\dfrac{5}{2}\))\(^2\)-\(\dfrac{13}{4}\)lớn hơn hoặc bằng -\(\dfrac{13}{4}\) với mọi x
=> min= -\(\dfrac{13}{4}\) <=> x = 5/2
5.
= 2( x\(^2\)-\(\dfrac{5}{2}\)x-\(\dfrac{1}{2}\))
=2( x\(^2\)-2.\(\dfrac{5}{4}\)+\(\dfrac{25}{4}\)-\(\dfrac{27}{4}\))
=2( x-\(\dfrac{5}{4}\))\(^2\)-\(\dfrac{27}{2}\) lớn hơn hoặc bằng -27/2 với mọi x
vậy min = -\(\dfrac{27}{2}\) <=> x= 5/4
![](https://rs.olm.vn/images/avt/0.png?1311)
ta có : \(A=x^2-2x+y^2-4y+6=\left(x^2-2x+1\right)+\left(y^2-4y+4\right)+1\)
\(A=\left(x-1\right)^2+\left(y-2\right)^2+1\)
ta có : \(\left(x-1\right)^2\ge0\) với mọi \(x\) và \(\left(y-2\right)^2\ge0\) với mọi \(y\)
\(\Rightarrow\left(x-1\right)^2+\left(y-2\right)^2+1\ge1\) với mọi \(x;y\)
\(\Rightarrow\) GTNN của \(A\) là 1 khi \(\left\{{}\begin{matrix}x-1=0\\y-2=0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\)
vậy giá trị nhỏ nhất của \(A\) là 1 khi \(x=1;y=2\)
A = \(x^2-2x+y^2-4y+6=x^2-2x+1+y^2-4y+4+1=\left(x-1\right)^2+\left(y-2\right)^2+1\ge1\)
Dấu ''='' xảy ra khi \(\left\{{}\begin{matrix}x-1=0\\y-2=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\)
Vậy GTNN của A là 1 khi x = 1 và y = 2
![](https://rs.olm.vn/images/avt/0.png?1311)
ĐK : \(x\ne-2\)
ta có \(A=\frac{x^2+2x+3}{\left(x+2\right)^2}=\frac{3x^2+6x+9}{3\left(x+2\right)^2}=\frac{2x^2+8x+8+x^2-2x+1}{3\left(x+2\right)^2}\)
\(=\frac{2\left(x+2\right)^2+\left(x-1\right)^2}{3\left(x+2\right)^2}=\frac{2}{3}+\frac{\left(x-1\right)^2}{3\left(x+2\right)^2}\)
vì (x-1)^2 >=0=> \(\frac{\left(x-1\right)^2}{3\left(x+2\right)^2}>=0\)
=> \(A>=\frac{2}{3}\)
dấu = xảy ra <=> x=1 ( thỏa mãn ĐKXĐ)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(A=x^2-5x+12\\ A=x^2-5x+\dfrac{25}{4}+\dfrac{23}{4}\\ A=\left(x^2-5x+\dfrac{25}{4}\right)+\dfrac{23}{4}\\ A=\left[x^2-2\cdot x\cdot\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2\right]+\dfrac{23}{4}\\ A=\left(x-\dfrac{5}{2}\right)^2+\dfrac{23}{4}\\ Do\text{ }\left(x-\dfrac{5}{2}\right)^2\ge0\forall x\\ \Rightarrow A=\left(x-\dfrac{5}{2}\right)^2+\dfrac{23}{4}\ge\dfrac{23}{4}\forall x\\ \text{Dấu "=" xảy ra khi : }\\ \left(x-\dfrac{5}{2}\right)^2=0\\ \Leftrightarrow x-\dfrac{5}{2}=0\\ \Leftrightarrow x=\dfrac{5}{2}\\ \text{Vậy }A_{\left(Min\right)}=\dfrac{23}{4}\text{ }khi\text{ }x=\dfrac{5}{2}\)
\(B=2x^2-14x+5\\ \\ A=2x^2-14x+\dfrac{49}{2}-\dfrac{39}{2}\\ A=\left(2x^2-14x+\dfrac{49}{2}\right)-\dfrac{39}{2}\\ A=2\left(x^2-7x+\dfrac{49}{4}\right)-\dfrac{39}{2}\\ A=\left[x^2-2\cdot x\cdot\dfrac{7}{2}+\left(\dfrac{7}{2}\right)^2\right]-\dfrac{39}{2}\\ A=\left(x-\dfrac{7}{2}\right)^2-\dfrac{39}{2}\\ Do\text{ }\left(x-\dfrac{7}{2}\right)^2\ge0\forall x\\ \Rightarrow A=\left(x-\dfrac{7}{2}\right)^2-\dfrac{39}{2}\ge-\dfrac{39}{2}\forall x\\ \text{Dấu "=" xảy ra khi : }\\ \left(x-\dfrac{7}{2}\right)^2=0\\ \Leftrightarrow x-\dfrac{7}{2}=0\\ \Leftrightarrow x=\dfrac{7}{2}\\ \text{Vậy }B_{\left(Min\right)}=-\dfrac{39}{2}\text{ }khi\text{ }x=\dfrac{7}{2}\)
\(B=2x^2-14x+5\\ B=2x^2-14x+\dfrac{49}{2}-\dfrac{39}{2}\\ B=\left(2x^2-14x+\dfrac{49}{2}\right)-\dfrac{39}{2}\\ B=2\left(x^2-7x+\dfrac{49}{4}\right)-\dfrac{39}{2}\\ B=2\left[x^2-2\cdot x\cdot\dfrac{7}{2}+\left(\dfrac{7}{2}\right)^2\right]-\dfrac{39}{2}\\ B=2\left(x-\dfrac{7}{2}\right)^2-\dfrac{39}{2}\\ \)
Do \(\left(x-\dfrac{7}{2}\right)^2\ge0\forall x\)
\(\Rightarrow2\left(x-\dfrac{7}{2}\right)^2\ge0\forall x\)
\(\Rightarrow B=2\left(x-\dfrac{7}{2}\right)^2-\dfrac{39}{2}\ge-\dfrac{39}{2}\forall x\)
Dấu \("="\) xảy ra khi :
\(\left(x-\dfrac{7}{2}\right)^2=0\\ \Leftrightarrow x-\dfrac{7}{2}=0\\ \Leftrightarrow x=\dfrac{7}{2}\)
Vậy \(B_{\left(Min\right)}=-\dfrac{39}{2}\) khi \(x=\dfrac{7}{2}\)
Do máy bị lỗi nên câu B bị trục trặc.
Mk xin lỗi.