\(B=25x^2+3y^2-10y+11\)

\(=25x^2+3\left(y^2-\frac{10}{3}y+\frac{11}{3}\right)\)

\(=25x^2+3\left(y^2-2.y.\frac{5}{3}+\frac{25}{9}+\frac{8}{9}\right)\)

\(=25x^2+3\left(y-\frac{5}{3}\right)^2+\frac{8}{3}\ge\frac{8}{3}\)

Đẳng thức xảy ra khi x = 0; y = 5/3

Vậy...

Đề có sai không bạn

TL
 

3y²+3y+25x²-10x+4

HT

TL:

3y² + 3y + 25x² - 10x + 4

~HT~

B= \(\frac{3y^2}{-25x^2+20xy-5y^2}=\frac{3y^2}{-y^2-\left(25x^2-20xy+4y^2\right)}=\frac{1}{-\frac{y^2}{3y^2}-\frac{\left(5x-2y\right)^2}{3y^2}}\)

=\(\frac{1}{-\frac{1}{3}-\frac{\left(5x-2y\right)^2}{3y^2}}\)

Có \(\frac{1}{3}+\frac{\left(5x-2y\right)^2}{3y^2}\ge\frac{1}{3}\) vs mọi x,y và y\(\ne0\)

<=>\(-\frac{1}{3}-\frac{\left(5x-2y\right)^2}{3y^2}\le-\frac{1}{3}\)

<=> \(\frac{1}{-\frac{1}{3}-\frac{\left(5x-2y\right)^2}{3y^2}}\ge-3\) <=> B \(\ge3\)

Dấu "=" xảy ra <=> 5x-2y=0

<=> 5x=2y < => \(x=\frac{2y}{5}\)

Vậy minB=3 <=> \(x=\frac{2y}{5}\)

A=\(25x^2+3y^2-10x+11=\)\(\left(5x\right)^2-2.5.x+1^2+3y^2+10=\)\(\left(5x+1\right)^2+3y^2+10\ge10\)

(Vì\(\left(5x+1\right)^2\ge0\forall x\),\(3y^2\ge0\forall y\))

Dấu "=" xảy ra \(\Leftrightarrow x=\frac{-1}{5},y=0\)

Vậy A max=10\(\Leftrightarrow x=\frac{-1}{5},y=0\)

_hì^^!!

camon bạn ạ

\(C=x^2-x+1=x^2-2.\frac{1}{2}.x+\frac{1}{4}+\frac{3}{4}=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}\)

Nên GTNN của C là \(\frac{3}{4}\) đặt được khi \(x-\frac{1}{2}=0\Leftrightarrow x=\frac{1}{2}\)

\(D=25x^2+3y^2-10xy+4y+1\)

\(=\left(5x\right)^2-2.5x.y+y^2+2y^2+4y+2-1\)

\(=\left(5x-y\right)^2+2\left(y+1\right)^2-1\ge-1\)

Nên GTNN của D là - 1  đạt được khi \(\hept{\begin{cases}y+1=0\\5x-y=0\end{cases}\Leftrightarrow}\hept{\begin{cases}y=-1\\y=5x\end{cases}\Leftrightarrow}\hept{\begin{cases}y=-1\\x=-\frac{1}{5}\end{cases}}\)