Sao ko cóp phần sau z

tìm min thì tách thích hợp ra toàn phương

\(B=2x^2+9y^2-6xy-6x-12y+2016\)

\(=x^2-6xy+9y^2+4x-12y+4+x^2-10x+25+1987\)

\(=\left(x-3y\right)^2+4\left(x-3y\right)+4+\left(x-5\right)^2+1987\)

\(=\left(x-3y+2\right)^2+\left(x-5\right)^2+1987\)

Vì \(\left(x-3y+2\right)^2\ge0\) và \(\left(x-5\right)^2\ge0\) nên GTNN của B là 1987, đạt được khi

\(\begin{cases}x-3y+2=0\\x-5=0\end{cases}\Leftrightarrow\begin{cases}y=\frac{7}{3}\\x=5\end{cases}}\)

\(2x^2+9y^2-6xy-6x-12y+2008\)

\(=\left(x^2-6xy+9y^2\right)+\left(4x-12y\right)+4+\left(x^2-10x+25\right)+1979\)

\(=\left(x-3y\right)^2+4\left(x-3y\right)+4+\left(x-5\right)^2+1979\)

\(=\left(x-3y+2\right)^2+\left(x-5\right)^2+1979\ge1979\)

Dấu ''='' xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x=5\\y=\frac{7}{3}\end{matrix}\right.\)

56% của 5789 kg là :

5789 x 56% = 3241,84 kg

Đáp số : 3241,84 kg

\(A=9y^2-6xy-12y+2x^2-6x+2016\)

\(A=\left(3y\right)^2-2.3y\left(x+2\right)+\left(x+2\right)^2-\left(x^2+4x+4\right)+2x^2-6x+2016\)

\(A=\left(3y-\left(x+2\right)\right)^2+x^2-10x+2012\)

\(A=\left(3y-x-2\right)^2+\left(x-5\right)^2+1987\)

Vậy GTNN của A = 1987 khi x=5 và y=7/3.

câu trả lời ngắn gọn thôi

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\(2x^2+9y^2-6xy-6x-12y+2004\)

\(=x^2-10x+25+x^2+9y^2+4-6xy+4x-12y+1975\)

\(=\left(x-5\right)^2+\left(x-3y+2\right)^2+1975\ge1975\)

Dấu \(=\)khi \(\hept{\begin{cases}x-5=0\\x-3y+2=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=5\\y=\frac{7}{3}\end{cases}}\).

=-12y

**** cho mình nha Thần Thánh

Q= 2x²+9y²-6xy-6x-12y+2015

=(x²-6xy+9y²-12y+4+4x)+(x²-10x+25)+1986

=(x-3y+2)²+(x-5)²+1986

Do (x-3y+2)²>0

(x-5)²>0

=>(x-3y+2)²+(x-5)²+1986>1986

=>Min Q=1986 <=>(x-3y+2)²=0 và (x-5)²=0

<=>x=5 và y=7/3

mình viết nhầm x^2 - 6xy + 9y^2 = (x - 3y)^2

Dòng thứ 2 là dùng hằng đẳng thức: (x+y+z)² = x² + y² + z² +2(xy + xz + yz)

Đề bài là gì vậy bạn?