Từ gt => \(\hept{\begin{cases}\left(\frac{1}{\sqrt{2}}-\sqrt{x}\right)\left(\frac{1}{\sqrt{2}}-\sqrt{y}\right)\ge0\Leftrightarrow\sqrt{x}+\sqrt{y}\le\frac{\sqrt{2}}{2}+\sqrt{2}\sqrt{xy}\left(1\right)\\x\sqrt{x}\le x\cdot\frac{1}{\sqrt{2}};y\sqrt{y}\le y\cdot\frac{1}{\sqrt{2}}\Rightarrow x\sqrt{x}+y\sqrt{y}\le\frac{1}{\sqrt{2}}\left(x+y\right)\left(2\right)\end{cases}}\)

Lại có \(\hept{\begin{cases}\sqrt{xy}\le xy+\frac{1}{4}\\\sqrt{xy}\le\frac{x+y}{2}\end{cases}\Rightarrow\hept{\begin{cases}\frac{2\sqrt{2}}{3}\sqrt{xy}\le\frac{2\sqrt{2}}{3}\left(xy+\frac{1}{4}\right)\left(3\right)\\\frac{\sqrt{2}}{3}\sqrt{xy}\le\frac{\sqrt{2}}{6}\left(x+y\right)\left(4\right)\end{cases}}}\)

Từ (1)(2)(3)(4) ta có:\(x\sqrt{x}+y\sqrt{y}+\sqrt{x}+\sqrt{y}\le\frac{\sqrt{2}}{2}\left(x+y\right)+\frac{\sqrt{2}}{2}+\frac{2\sqrt{2}}{3}\left(xy+\frac{1}{4}\right)+\frac{\sqrt{2}}{6}\left(x+y\right)\)

\(\le\frac{2\sqrt{2}}{3}\left(1+x+y+xy\right)\)

=> \(VT=\frac{\sqrt{x}}{1+y}+\frac{\sqrt{y}}{1+x}=\frac{x\sqrt{x}+y\sqrt{y}+\sqrt{x}+\sqrt{y}}{1+x+y+xy}\le\frac{2\sqrt{2}}{3}\)

Dấu "=" xảy ra <=> x=y=\(\frac{1}{2}\)

Đk : 1 < = x < = 5

B^2 = x-1+5-x + 2.\(\sqrt{\left(x-1\right)\left(5-x\right)}\)

Áp dụng bđt cosi thì :

B^2 >= 4 + x-1+5-x = 8

=>B < = 2\(\sqrt{2}\)

Vậy Max B = 2\(\sqrt{2}\)<=> x=1

k mk nha

mk hc nghu lém mk giải ko dc nhưng cho mk xin nha mấy bn yêu mấy bn nh`

x=5 y=15

cái này là giải hpt rồi

con lậy hỏi thế bố đứa nào trả lời được trừ Tuấn Anh

The savory melt-in-your-mouth cheese; the sweet sauce; the fluffy yet crispy crust. When joined together on a pizza pan, the combination of flavors and textures is one that few of us can say "no" to. In fact, in an Eat This, Not That! survey of more than 10,000 readers, approximately 40 percent of respondents said that of all the guilty food pleasures on the planet, pizza is the one thing they could never, ever give up. Which we can't say was all too shocking to learn. Every day about 40 million people across America sit down to enjoy a slice. And while there are tons of reasons why our nation has such a high obesity rate, we can't help but wonder how large of a role all that pepperoni and cheese-stuffed crust are playing.

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