Các chuyên đề toán HSG lớp 9

[light_future96]

Số chinh Phương ôn chuyên
[PDF]https://upload.butnghien.vn/files/0lynow1eajwkjuwmx2lu.pdf[/PDF]

 

[light_future96]

Bất đẳng thức

[PDF]https://upload.butnghien.vn/files/7gru8b3vu40ljsttnoge.pdf[/PDF]

 

[light_future96]

Nguyên lí Đi rích lê

[PDF]https://upload.butnghien.vn/files/0l3uq1jmkudfd3cwcm3e.pdf[/PDF]

 

[light_future96]

\[(\frac{\sqrt{a}+3}{\sqrt{a}-3}-\frac{\sqrt{a}-3}{\sqrt{a}+3})\frac{1}{3}-\frac{1}{\sqrt{a}})\]
\[=(\frac{(\sqrt{a}+3)(\sqrt{a}+3)}{(\sqrt{a}-3)(\sqrt{a}+3)}+\frac{(\sqrt{a}-3)(\sqrt{a}-3)}{(\sqrt{a}-3)(\sqrt{a}+3)}):\frac{\sqrt{a}-3}{3\sqrt{a}}\]
\[=(\frac{({\sqrt{a}+3)}^{2}}{(\sqrt{a}-3)(\sqrt{a}+3)}+\frac{({\sqrt{a}-3)}^{2}}{(\sqrt{a}-3)(\sqrt{a}+3)}).\frac{3\sqrt{a}}{\sqrt{a}-3}\]
\[=(\frac{(a+6\sqrt{a}+9)-(a-6\sqrt{a}+9}{(\sqrt{a}-3)(\sqrt{a}+3)}).\frac{3\sqrt{a}}{\sqrt{a}-3}\]
\[=\frac{48a}{(a-9)(\sqrt{a-3}}\]