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1) ( V 1,3 + V 13 )( V 13 - V 1,3 ) = ( V 13 )^2 - ( V 1,3 )^2 = 13 - 1,3 = 11,7
2) ( 5 + V 2 )^2 = 25 + 10V2 + 2 = 27 + 10V2
3) 11,7 - 27 - 10V2 + 10V2 = - 15,3
Ответ ( - 15,3 )
2) ( 5 + V 2 )^2 = 25 + 10V2 + 2 = 27 + 10V2
3) 11,7 - 27 - 10V2 + 10V2 = - 15,3
Ответ ( - 15,3 )
Ответ дал:
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C.4.73.
1)
![(2+sqrt{7})(sqrt{7}-2)-(5+sqrt{2})^2+10sqrt{2}=\(sqrt{7})^2-2^2-(5^2+2*5sqrt{2}+(sqrt{2})^2)+10sqrt{2}=\7-4-(25+10sqrt{2}+2)+10sqrt{2}=3-25-10sqrt{2}-2+10sqrt{2}=-24 (2+sqrt{7})(sqrt{7}-2)-(5+sqrt{2})^2+10sqrt{2}=\(sqrt{7})^2-2^2-(5^2+2*5sqrt{2}+(sqrt{2})^2)+10sqrt{2}=\7-4-(25+10sqrt{2}+2)+10sqrt{2}=3-25-10sqrt{2}-2+10sqrt{2}=-24](https://tex.z-dn.net/?f=%282%2Bsqrt%7B7%7D%29%28sqrt%7B7%7D-2%29-%285%2Bsqrt%7B2%7D%29%5E2%2B10sqrt%7B2%7D%3D%5C%28sqrt%7B7%7D%29%5E2-2%5E2-%285%5E2%2B2%2A5sqrt%7B2%7D%2B%28sqrt%7B2%7D%29%5E2%29%2B10sqrt%7B2%7D%3D%5C7-4-%2825%2B10sqrt%7B2%7D%2B2%29%2B10sqrt%7B2%7D%3D3-25-10sqrt%7B2%7D-2%2B10sqrt%7B2%7D%3D-24)
2)
![frac{2}{7}sqrt{5}*1frac{3}{4}sqrt{5}+(sqrt{25^0}-2)^2=frac{2}{7}*frac{7}{4}*(sqrt{5})^2+(sqrt{1}-2)^2=\frac{5}{2}+(-1)^2=2,5+1=3,5 frac{2}{7}sqrt{5}*1frac{3}{4}sqrt{5}+(sqrt{25^0}-2)^2=frac{2}{7}*frac{7}{4}*(sqrt{5})^2+(sqrt{1}-2)^2=\frac{5}{2}+(-1)^2=2,5+1=3,5](https://tex.z-dn.net/?f=frac%7B2%7D%7B7%7Dsqrt%7B5%7D%2A1frac%7B3%7D%7B4%7Dsqrt%7B5%7D%2B%28sqrt%7B25%5E0%7D-2%29%5E2%3Dfrac%7B2%7D%7B7%7D%2Afrac%7B7%7D%7B4%7D%2A%28sqrt%7B5%7D%29%5E2%2B%28sqrt%7B1%7D-2%29%5E2%3D%5Cfrac%7B5%7D%7B2%7D%2B%28-1%29%5E2%3D2%2C5%2B1%3D3%2C5)
3)
![frac{5}{3-2sqrt{2}}+frac{5}{3+2sqrt{2}}=frac{5(3+2sqrt{2})}{(3-2sqrt{2})(3+2sqrt{2})}+frac{5(3-2sqrt{2})}{(3+2sqrt{2})(3-2sqrt{2})}=\frac{5(3+2sqrt{2})+5(3-2sqrt{2})}{(3-2sqrt{2})(3+2sqrt{2})}=frac{5(3+2sqrt{2}+3-2sqrt{2})}{3^2-(2sqrt{2})^2}=frac{5*6}{9-8}=30 frac{5}{3-2sqrt{2}}+frac{5}{3+2sqrt{2}}=frac{5(3+2sqrt{2})}{(3-2sqrt{2})(3+2sqrt{2})}+frac{5(3-2sqrt{2})}{(3+2sqrt{2})(3-2sqrt{2})}=\frac{5(3+2sqrt{2})+5(3-2sqrt{2})}{(3-2sqrt{2})(3+2sqrt{2})}=frac{5(3+2sqrt{2}+3-2sqrt{2})}{3^2-(2sqrt{2})^2}=frac{5*6}{9-8}=30](https://tex.z-dn.net/?f=frac%7B5%7D%7B3-2sqrt%7B2%7D%7D%2Bfrac%7B5%7D%7B3%2B2sqrt%7B2%7D%7D%3Dfrac%7B5%283%2B2sqrt%7B2%7D%29%7D%7B%283-2sqrt%7B2%7D%29%283%2B2sqrt%7B2%7D%29%7D%2Bfrac%7B5%283-2sqrt%7B2%7D%29%7D%7B%283%2B2sqrt%7B2%7D%29%283-2sqrt%7B2%7D%29%7D%3D%5Cfrac%7B5%283%2B2sqrt%7B2%7D%29%2B5%283-2sqrt%7B2%7D%29%7D%7B%283-2sqrt%7B2%7D%29%283%2B2sqrt%7B2%7D%29%7D%3Dfrac%7B5%283%2B2sqrt%7B2%7D%2B3-2sqrt%7B2%7D%29%7D%7B3%5E2-%282sqrt%7B2%7D%29%5E2%7D%3Dfrac%7B5%2A6%7D%7B9-8%7D%3D30)
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