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mnogozadachnik
@mnogozadachnik
July 2022
1
3
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№3 Сократить дробь
а)[tex]\frac{7+\sqrt{7} }{5\sqrt{7} }[/tex] б)[tex]\frac{16p-5}{4\sqrt{p}-\sqrt{5} }[/tex]
№4 Освободитесь от иррациональности в знаменателе
а)[tex]\frac{4}{2\sqrt{6} }[/tex] б)[tex]\frac{10}{3-\sqrt{5} }[/tex]
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daraprelj
№3.а)
№3.б)
№4.а)
№4.б)
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Answers & Comments
№3.а)![\displaystyle \frac{7+\sqrt{7} }{5\sqrt{7} } = \frac{\sqrt{7}*(\sqrt{7} +1) }{5\sqrt{7} }=\frac{\sqrt{7} +1 }{5 } \displaystyle \frac{7+\sqrt{7} }{5\sqrt{7} } = \frac{\sqrt{7}*(\sqrt{7} +1) }{5\sqrt{7} }=\frac{\sqrt{7} +1 }{5 }](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B7%2B%5Csqrt%7B7%7D%20%7D%7B5%5Csqrt%7B7%7D%20%7D%20%3D%20%5Cfrac%7B%5Csqrt%7B7%7D%2A%28%5Csqrt%7B7%7D%20%2B1%29%20%7D%7B5%5Csqrt%7B7%7D%20%7D%3D%5Cfrac%7B%5Csqrt%7B7%7D%20%2B1%20%7D%7B5%20%7D)
№3.б)![\displaystyle \frac{16p-5}{4\sqrt{p}-\sqrt{5} } =\frac{(4\sqrt{p}+\sqrt{5} )(4\sqrt{p}-\sqrt{5} )}{4\sqrt{p}-\sqrt{5} } =4\sqrt{p}+\sqrt{5} \displaystyle \frac{16p-5}{4\sqrt{p}-\sqrt{5} } =\frac{(4\sqrt{p}+\sqrt{5} )(4\sqrt{p}-\sqrt{5} )}{4\sqrt{p}-\sqrt{5} } =4\sqrt{p}+\sqrt{5}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B16p-5%7D%7B4%5Csqrt%7Bp%7D-%5Csqrt%7B5%7D%20%20%7D%20%3D%5Cfrac%7B%284%5Csqrt%7Bp%7D%2B%5Csqrt%7B5%7D%20%29%284%5Csqrt%7Bp%7D-%5Csqrt%7B5%7D%20%29%7D%7B4%5Csqrt%7Bp%7D-%5Csqrt%7B5%7D%20%20%7D%20%3D4%5Csqrt%7Bp%7D%2B%5Csqrt%7B5%7D)
№4.а)![\displaystyle \frac{4}{2\sqrt{6} } *\frac{\sqrt{6}}{\sqrt{6}} =\frac{4\sqrt{6}}{2*6} =\frac{\sqrt{6}}{3} \displaystyle \frac{4}{2\sqrt{6} } *\frac{\sqrt{6}}{\sqrt{6}} =\frac{4\sqrt{6}}{2*6} =\frac{\sqrt{6}}{3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B4%7D%7B2%5Csqrt%7B6%7D%20%7D%20%2A%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B%5Csqrt%7B6%7D%7D%20%3D%5Cfrac%7B4%5Csqrt%7B6%7D%7D%7B2%2A6%7D%20%3D%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B3%7D)
№4.б)![\displaystyle \frac{10}{3-\sqrt{5} } *\frac{3+\sqrt{5}}{3+\sqrt{5}}=\frac{10*(3+\sqrt{5})}{(3-\sqrt{5})(3+\sqrt{5})}=\frac{10*(3+\sqrt{5}) }{9-5} =\frac{10*(3+\sqrt{5}) }{4} =\frac{5*(3+\sqrt{5}) }{2} =\frac{15+5\sqrt{3} }{2} \displaystyle \frac{10}{3-\sqrt{5} } *\frac{3+\sqrt{5}}{3+\sqrt{5}}=\frac{10*(3+\sqrt{5})}{(3-\sqrt{5})(3+\sqrt{5})}=\frac{10*(3+\sqrt{5}) }{9-5} =\frac{10*(3+\sqrt{5}) }{4} =\frac{5*(3+\sqrt{5}) }{2} =\frac{15+5\sqrt{3} }{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B10%7D%7B3-%5Csqrt%7B5%7D%20%7D%20%2A%5Cfrac%7B3%2B%5Csqrt%7B5%7D%7D%7B3%2B%5Csqrt%7B5%7D%7D%3D%5Cfrac%7B10%2A%283%2B%5Csqrt%7B5%7D%29%7D%7B%283-%5Csqrt%7B5%7D%29%283%2B%5Csqrt%7B5%7D%29%7D%3D%5Cfrac%7B10%2A%283%2B%5Csqrt%7B5%7D%29%20%7D%7B9-5%7D%20%3D%5Cfrac%7B10%2A%283%2B%5Csqrt%7B5%7D%29%20%7D%7B4%7D%20%3D%5Cfrac%7B5%2A%283%2B%5Csqrt%7B5%7D%29%20%7D%7B2%7D%20%3D%5Cfrac%7B15%2B5%5Csqrt%7B3%7D%20%7D%7B2%7D)