a)

\(A=4x-x^2+3=-\left(x^2-4x-3\right)=-\left(x^2-4x+4\right)+7=-\left(x-2\right)^2+7\le7\)

Daaus = xayr ra khi: x = 2

b) \(B=4x^2-12x+15=4\left(x^2-3x+9\right)-21=4\left(x-3\right)^2-21\ge-21\)

Dấu = xảy ra khi x = 3

c) \(C=4x^2+2y^2-4xy-4y+1=\left(4x^2-4xy+y^2\right)+\left(y^2-4y+4\right)-3=\left(2x-y\right)^2+\left(y-2\right)^2-3\ge-3\)

Dấu = xảy ra khi

2x = y và y = 2

=> x = 1 và y = 2

a) A = \(-x^2+4x+3=-\left(x-2\right)^2+7\le7\)

Dấu "=" <=> x = 2

b) \(4x^2-12x+15=\left(2x-3\right)^2+6\ge6\)

Dấu "=" xảy ra <=> \(x=\dfrac{3}{2}\)

c) \(4x^2+2y^2-4xy-4y+1\)

= \(\left(4x^2-4xy+y^2\right)+\left(y^2-4y+4\right)-3\)

= \(\left(2x-y\right)^2+\left(y-2\right)^2-3\ge-3\)

Dấu "=" <=> \(\left\{{}\begin{matrix}x=1\\y=2\end{matrix}\right.\)

a) A= 2x²-8x+10 = 2(x-2)²+2\(\ge\)2\(\Leftrightarrow\)x=2

Vậy MinA=2 \(\Leftrightarrow\)x=2

b) B= -(x-1)²-(2y+1)²+7 \(\le\)7

Dấu = xảy ra khi x=1 và y=\(\frac{-1}{2}\)

Vậy MaxB=7 ....

cảm ơn bạn nha

Ai giúp mik vs

Huhu ai giúp vs

\(E=2x^2+5y^2+x+4y+5\)

\(\Rightarrow E=2x^2+x+5y^2+4y+5\)

\(\Rightarrow E=2\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}-\dfrac{1}{16}\right)+5\left(y^2+\dfrac{4}{5}y+\dfrac{4}{25}-\dfrac{4}{25}\right)+5\)

\(\Rightarrow E=2\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\right)+5\left(y^2+\dfrac{4}{5}y+\dfrac{4}{25}\right)+5-\dfrac{1}{8}-\dfrac{4}{5}\)

\(\Rightarrow E=2\left(x+\dfrac{1}{4}\right)^2+5\left(y+\dfrac{2}{5}\right)^2+\dfrac{163}{40}\)

mà \(\left\{{}\begin{matrix}2\left(x+\dfrac{1}{4}\right)^2\ge0,\forall x\\5\left(y+\dfrac{2}{5}\right)^2\ge0,\forall y\end{matrix}\right.\)

\(\Rightarrow E=2\left(x+\dfrac{1}{4}\right)^2+5\left(y+\dfrac{2}{5}\right)^2+\dfrac{163}{40}\ge\dfrac{163}{40}\)

\(\Rightarrow GTNN\left(E\right)=\dfrac{163}{40}\left(tạix=-\dfrac{1}{4};y=-\dfrac{2}{5}\right)\)

=x²-2xy+y²+4y²+4y+1+2

=(x-y)²+(2y+1)²+2\(\ge2\)

dấu bằng xảy ra khi x=y=-1/2

Ta có:

\(A=x^2+y^2+xy-2x-4y+2016\\ =\left(x+\dfrac{y}{2}-1\right)^2+\dfrac{3}{2}\left(y-1\right)^2+\dfrac{4027}{2}\\ \ge\dfrac{4027}{2}\)

Dấu bằng xảy ra khi và chỉ khi: 

\(\left\{{}\begin{matrix}x=\dfrac{1}{2}\\y=1\end{matrix}\right.\)

\(A=x^2+2x\left(y+1\right)+\left(y+1\right)^2-\left(y+1\right)^2+2y^2-4y+2028\)

\(=\left(x+y+1\right)^2-y^2-2x-1+2y^2-4y+2028\)

\(=\left(x+y+1\right)^2-6x+y^2+2027\)

\(=\left(x+y+1\right)+\left(y-3\right)^2+2018\ge2018\forall x;y\) (do...)

=> MinA = 2018 \(\Leftrightarrow\left\{{}\begin{matrix}x+y=-1\\y=3\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=-4\\y=3\end{matrix}\right.\)

`A=x^2+6x+y^2+4y+15`

`=(x^2+6x+9)+(y^2+4y+4)+2`

`=(x+3)^2+(y+2)^2+2`

Vì `(x+3)^2+(y+2)^2 >=0 forall x,y`

`=>A_(min)=2 <=> x=-3; y=-2`.

Ta có: \(A=x^2+6x+y^2+4y+15\)

\(=x^2+6x+9+y^2+4y+4+2\)

\(=\left(x+3\right)^2+\left(y+2\right)^2+2\ge2\forall x,y\)

Dấu '=' xảy ra khi (x,y)=(-3;-2)

x² - 2x + y² - 4y + 7 = (x² - 2x + 1) + ( y² - 4y + 4) + 2 = (x - 1)² + (y - 2)² + 2

Vì (x - 1)² ≥ 0 \(\forall\)x

    (y - 2)² ≥ 0 \(\forall\)x

=> (x - 1)² + (y - 2)² ≥ 0 \(\forall\)x

=> (x - 1)² + (y - 2)² + 2  ≥ 2 

Dấu " = " xảy ra <=> \(\hept{\begin{cases}\left(x-1\right)^2=0\\\left(y-2\right)^2=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x-1=0\\y-2=0\end{cases}\Leftrightarrow}\hept{\begin{cases}x=1\\y=2\end{cases}}\)

Vậy GTNN của x² - 2x + y² - 4y +7 = 2 khi x = 1; y = 2

Đặt \(A=x^2-2x+y^2-4y+7\)

\(\Rightarrow A=\left(x^2-2x+1\right)+\left(y^2-4y+4\right)+2\)

\(=\left(x-1\right)^2+\left(y-2\right)^2+2\)

Vì \(\left(x-1\right)^2\ge0\forall x\); \(\left(y-2\right)^2\ge0\forall y\)

\(\Rightarrow\left(x-1\right)^2+\left(y-2\right)^2\ge0\forall x,y\)

\(\Rightarrow\left(x-1\right)^2+\left(y-2\right)^2+2\ge2\forall x,y\)

hay \(A\ge2\)

Dấu " = " xảy ra \(\Leftrightarrow\hept{\begin{cases}x-1=0\\y-2=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=1\\y=2\end{cases}}\)

Vậy \(minA=2\)\(\Leftrightarrow\hept{\begin{cases}x=1\\y=2\end{cases}}\)