Mik có lớp 4 thôi seo giúp đc . Seo bn zô zuyên hế . ^~^

xin lỗi nhé

ta có :

\(P=\left(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{xy}+\sqrt{x}+1-\sqrt{xy}}{1-\sqrt{xy}}\right):\left(\frac{\sqrt{xy}-1-\sqrt{xy}-\sqrt{x}}{\sqrt{xy}-1}-\frac{\sqrt{x}+1}{\sqrt{xy}+1}\right)\)

\(=\left(\frac{\sqrt{x}+1}{\sqrt{xy}+1}+\frac{\sqrt{x}+1}{1-\sqrt{xy}}\right):\left(\frac{1+\sqrt{x}}{1-\sqrt{xy}}-\frac{1+\sqrt{x}}{\sqrt{xy}+1}\right)\)

\(=\left(\frac{1}{\sqrt{xy}+1}+\frac{1}{1-\sqrt{xy}}\right):\left(\frac{1}{1-\sqrt{xy}}-\frac{1}{\sqrt{xy}+1}\right)\)

\(=\frac{2}{1-xy}:\text{​​}\frac{2\sqrt{xy}}{1-xy}=\frac{1}{\sqrt{xy}}\)

b.ta có \(P=\frac{1}{\sqrt{xy}}\le\frac{\left(\frac{1}{\sqrt{x}}+\frac{1}{\sqrt{y}}\right)^2}{4}=\frac{36}{4}=9\)

Vậy GTLN của P =9

oh no oh no oh no oh no no no no no

oh no oh no oh no no no no no

\(ĐKXĐ:x\ge3\)

\(2\sqrt{9x-27}-\frac{1}{5}\sqrt{25x-75}-\frac{1}{7}\sqrt{49x-147}=0\)

\(2\sqrt{9\left(x-3\right)}-\frac{1}{5}\sqrt{25\left(x-3\right)}-\frac{1}{7}\sqrt{49\left(x-3\right)}=0\)

\(6\sqrt{x-3}-\sqrt{x-3}-\sqrt{x-3}=0\)

\(4\sqrt{x-3}=0\)

\(x-3=0\)

\(x=3\left(TM\right)\)

\(\sqrt{x-3}-2\sqrt{x^2-9}=0\)ĐK : \(x\le-3;x\ge3\)

\(\Leftrightarrow\sqrt{x-3}\left(1-2\sqrt{x+3}\right)=0\)

TH1 : \(\sqrt{x-3}=0\Leftrightarrow x-3=0\Leftrightarrow x=3\)(tm)

TH2 : \(1-2\sqrt{x+3}=0\Leftrightarrow2\sqrt{x+3}=1\)

\(\Leftrightarrow4\left(x+3\right)=1\Leftrightarrow x+3=\frac{1}{4}\Leftrightarrow x=-\frac{11}{4}\)(ktm) 

\(ĐKXĐ:x\ge3\)

\(\sqrt{x-3}-2\sqrt{x^2-9}=0\)

\(\sqrt{x-3}-2\sqrt{\left(x-3\right)}\sqrt{\left(x+3\right)}=0\)

\(\sqrt{x-3}\left(1-2\sqrt{x+3}\right)=0\)

\(\orbr{\begin{cases}\sqrt{x-3}=0\\1-2\sqrt{x+3}=0\end{cases}\orbr{\begin{cases}x=3\\\sqrt{x+3}=\frac{1}{2}\end{cases}\orbr{\begin{cases}x=3\\x+3=\frac{1}{4}\end{cases}\orbr{\begin{cases}x=3\left(TM\right)\\x=-\frac{11}{4}\left(KTM\right)\end{cases}}}}}\)

7sin²a+5cos²a=13/2

2sin²a+(5sin²a+5cos²a)=13/2

2sin²a+5=13/2(do sin²a+cos²a=1, công thức này bạn có thể xem chứng minh trên youtube nha, cái này ai cũng phải biết)

2sin²a=3/2

sin²a=3/4

sin(a)=\(\frac{\sqrt{3}}{2}\)

suy ra a=60⁰