1 - а)
Если вы ещё не проходили, что корень может быть как положительным, так и отрицательным (например
![\sqrt4=2,\;\sqrt4=-2](https://tex.z-dn.net/?f=%5Csqrt4%3D2%2C%5C%3B%5Csqrt4%3D-2)
), то ещё и в)
![2.\;a)\;\sqrt{\frac{256}{100}}+\sqrt{\frac{81}{100}}=\frac{16}{10}+\frac9{10}=\frac{25}{10}=2,5\\b)\;\sqrt{\frac9{144}}-\sqrt{\frac1{16}}=\frac3{12}-\frac14=\frac3{12}-\frac3{12}=0](https://tex.z-dn.net/?f=2.%5C%3Ba%29%5C%3B%5Csqrt%7B%5Cfrac%7B256%7D%7B100%7D%7D%2B%5Csqrt%7B%5Cfrac%7B81%7D%7B100%7D%7D%3D%5Cfrac%7B16%7D%7B10%7D%2B%5Cfrac9%7B10%7D%3D%5Cfrac%7B25%7D%7B10%7D%3D2%2C5%5C%5Cb%29%5C%3B%5Csqrt%7B%5Cfrac9%7B144%7D%7D-%5Csqrt%7B%5Cfrac1%7B16%7D%7D%3D%5Cfrac3%7B12%7D-%5Cfrac14%3D%5Cfrac3%7B12%7D-%5Cfrac3%7B12%7D%3D0)
![3.\;a)\sqrt{98x^6y^5}=\sqrt{2\cdot49x^6y^5}=7x^3y^2\sqrt y\\b)\;\frac2x\sqrt{\frac1{16}x^6}=\sqrt{\frac4{x^2}\cdot\frac1{16}x^6}=\sqrt{\frac14x^4}](https://tex.z-dn.net/?f=3.%5C%3Ba%29%5Csqrt%7B98x%5E6y%5E5%7D%3D%5Csqrt%7B2%5Ccdot49x%5E6y%5E5%7D%3D7x%5E3y%5E2%5Csqrt+y%5C%5Cb%29%5C%3B%5Cfrac2x%5Csqrt%7B%5Cfrac1%7B16%7Dx%5E6%7D%3D%5Csqrt%7B%5Cfrac4%7Bx%5E2%7D%5Ccdot%5Cfrac1%7B16%7Dx%5E6%7D%3D%5Csqrt%7B%5Cfrac14x%5E4%7D)
![4.\;a)\;\frac{2}{12-\sqrt3}=\frac{2(12+\sqrt3)}{(12-\sqrt3)(12+\sqrt3)}=\frac{24+2\sqrt3}{144-3}=\frac{24+2\sqrt3}{141}\\b)\;\frac{18}{\sqrt{10}-\sqrt2}=\frac{18(\sqrt{10}+\sqrt2)}{(\sqrt{10}-\sqrt2)(\sqrt{10}+\sqrt2)}=\frac{18(\sqrt{10}+\sqrt2)}{10-2}=\frac{18(\sqrt{10}+\sqrt2)}{8}=\\=\frac{9(\sqrt{10}+\sqrt2)}4](https://tex.z-dn.net/?f=4.%5C%3Ba%29%5C%3B%5Cfrac%7B2%7D%7B12-%5Csqrt3%7D%3D%5Cfrac%7B2%2812%2B%5Csqrt3%29%7D%7B%2812-%5Csqrt3%29%2812%2B%5Csqrt3%29%7D%3D%5Cfrac%7B24%2B2%5Csqrt3%7D%7B144-3%7D%3D%5Cfrac%7B24%2B2%5Csqrt3%7D%7B141%7D%5C%5Cb%29%5C%3B%5Cfrac%7B18%7D%7B%5Csqrt%7B10%7D-%5Csqrt2%7D%3D%5Cfrac%7B18%28%5Csqrt%7B10%7D%2B%5Csqrt2%29%7D%7B%28%5Csqrt%7B10%7D-%5Csqrt2%29%28%5Csqrt%7B10%7D%2B%5Csqrt2%29%7D%3D%5Cfrac%7B18%28%5Csqrt%7B10%7D%2B%5Csqrt2%29%7D%7B10-2%7D%3D%5Cfrac%7B18%28%5Csqrt%7B10%7D%2B%5Csqrt2%29%7D%7B8%7D%3D%5C%5C%3D%5Cfrac%7B9%28%5Csqrt%7B10%7D%2B%5Csqrt2%29%7D4)
-1,2,5... найти S50 - ?
a1 = -1, a2 = 2, d = -3, n = 50 , где a1,2 - члены прогрессии, n - количество членов прогрессии, d - разность (рассчитывается как a2 - a1)
Сначала находим an по формуле:
an = a1+(n-1)*d = -1 + (50 - 1) *(-3) = -1 + (49 *(-3)) = -1 - 147 = -148
Теперь находим S50 по формуле:
S50 = a1 + an * n / 2 = -1 -148 * 50 / 2 = -149 * 25 = -3725
Ответ: S50 = -3725