sol của tớ :3

Nếu y=0 thì x²=1 => P=2

Nếu y\(\ne\)0 .Đặt \(t=\frac{x}{y}\)

\(P=\frac{2\left(x^2+6xy\right)}{1+2xy+2y^2}=\frac{2\left(x^2+6xy\right)}{x^2+2xy+3y^2}=\frac{2\left[\left(\frac{x}{y}\right)^2+6\cdot\frac{x}{y}\right]}{\left(\frac{x}{y}\right)^2+2\frac{x}{y}+3}=\frac{2\left(t^2+6t\right)}{t^2+2t+3}\)

\(\Rightarrow P.t^2+2P\cdot t+3P=2t^2+12t\)

\(\Leftrightarrow t^2\left(P-2\right)+2t\left(P-6\right)+3P=0\)

Xét \(\Delta'=\left(P-2\right)^2-3P\left(P-6\right)=-2P^2-6P+36\ge0\)

\(\Leftrightarrow-6\le P\le3\)

Dấu bằng xảy ra khi:

Max:\(x=\frac{3}{\sqrt{10}};y=\frac{1}{\sqrt{10}}\left(h\right)x=\frac{3}{-\sqrt{10}};y=\frac{1}{-\sqrt{10}}\)

Min:\(x=\frac{3}{\sqrt{13}};y=-\frac{2}{\sqrt{13}}\left(h\right)x=-\frac{3}{\sqrt{13}};y=\frac{2}{\sqrt{13}}\)

khó ha

Ta co:

\(P=\frac{2x^2+12xy}{1+2xy+2y^2}\)

\(\Leftrightarrow Px^2+Py^2+2Pxy+2Py^2=2x^2+12xy\)

\(\Leftrightarrow\left(P-2\right)x^2+\left(2P-12\right)xy+3Py^2=0\)

\(\Leftrightarrow\left(P-2\right)\frac{x^2}{y^2}+\left(2P-12\right)\frac{x}{y}+3P=0\)

Dat \(\frac{x}{y}=t\left(t\in R\right)\)

PT tro thanh

\(\left(P-2\right)t^2+\left(2P-12\right)t+2P=0\)

Xet \(P=2\)\(\Rightarrow x=\frac{5}{4};y=\frac{5}{3}\)

Xet \(P\ne2\)

Ta lai co:

\(\Delta^`\ge0\)

\(\Leftrightarrow\left(P-6\right)^2-\left(P-2\right).2P\ge0\)

\(\Leftrightarrow-P^2-8P+36\ge0\)

\(\Leftrightarrow P^2+8P-36\le0\)

\(\Leftrightarrow\left(P+4-2\sqrt{13}\right)\left(P+4+2\sqrt{13}\right)\le0\)

TH1:

\(\hept{\begin{cases}P+4-2\sqrt{13}\ge0\\P+4+2\sqrt{13}\le0\end{cases}\left(l\right)}\)

TH2:

\(\hept{\begin{cases}P+4-2\sqrt{13}\le0\\P+4+2\sqrt{13}\ge0\end{cases}\Leftrightarrow-4-2\sqrt{13}\le P\le2\sqrt{13}-4}\)

Dau '=' xay ra khi \(\frac{x}{y}=\frac{10-2\sqrt{13}}{2\sqrt{13}-6}\Leftrightarrow\Leftrightarrow\hept{\begin{cases}x=\frac{1}{\sqrt{1+\left(\frac{\text{ }2\sqrt{13}-6}{10-2\sqrt{13}}\right)^2}}\\y=\frac{2\sqrt{13}-6}{\left(10-2\sqrt{13}\right)\sqrt{1+\left(\frac{2\sqrt{13}-6}{10-2\sqrt{13}}\right)^2}}\end{cases}}\)

Cho dau '=' xay ra khung chac dung khong nua

khó thật sự!!

lớp mấy dậy bạn

Đẳng thức xảy ra khi 

Đẳng thức xảy ra khi 

P/s: Mình làm ra số đẹp mà nhỉ?

khó quá đi thôi

Khó lắm luôn á

khos vaayj

hhshsuui

hhs gkbhnsf

Kho nhi

Lam the nao nhi

làm gì đây

xây bằng phân à 

fghjklaha

Đố ai trả lời  được

nnhgj gynmikjijnjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjjs

đống hánh hdggy vawi cả lín hhgtg ok

đống phâ nn

Khổ quá tao không thích trả lời đâu . Tao bị đau đầu nhen mày

bị lừa rồi nhé

isnuijhjihjijk,.ư

ikoksojr25kjngghghgashsggssggggttddfytddtftgyshbgbmnhffrrddfwwfrrwrtwtgtwdrdr4seqdx jvvvsgfgjfgfggjghhghdgdhjhh

nefffffdvdfgygyrghydkgykuuiguii45gyeggytjy

httgyhthtynty33rhy4hgy77tyy7hangnsirgxyygbut756tyuygugyi

làm gì đây. xây chùa môt cột à

Đỗ huy đang ỉa trong nhà

đói bụng

Má ơi , sao ai gửi vậy

hrgggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb