Ответы
Ответ дал:
0
№4 из 1-го варианта
Решаю по действиям.
1)![sqrt{11-6 sqrt{2} }= sqrt{9-6 sqrt{2} +2} = sqrt{3^2-2*3* sqrt{2} +( sqrt{2} )^2} = sqrt{11-6 sqrt{2} }= sqrt{9-6 sqrt{2} +2} = sqrt{3^2-2*3* sqrt{2} +( sqrt{2} )^2} =](https://tex.z-dn.net/?f=+sqrt%7B11-6+sqrt%7B2%7D+%7D%3D+sqrt%7B9-6+sqrt%7B2%7D+%2B2%7D++%3D+sqrt%7B3%5E2-2%2A3%2A+sqrt%7B2%7D+%2B%28+sqrt%7B2%7D+%29%5E2%7D+%3D+)
![sqrt{(3- sqrt{2} )^2} =3- sqrt{2} sqrt{(3- sqrt{2} )^2} =3- sqrt{2}](https://tex.z-dn.net/?f=+sqrt%7B%283-+sqrt%7B2%7D+%29%5E2%7D+%3D3-+sqrt%7B2%7D+)
2) (6+2√2)·(3-√2) = 2·(3+√2)·(3-√2) = 2·(3²-√2²) = 2 · (9 - 2) = 2 · 7 = 14
3)![4,5- sqrt{14} = frac{9}{2}- sqrt{14} = frac{9-2 sqrt{14} }{2} = frac{7-2 sqrt{7} sqrt{2} +2}{2} = frac{ sqrt{7} ^2-2 sqrt{7} * sqrt{2} + sqrt{2} ^2}{2} = 4,5- sqrt{14} = frac{9}{2}- sqrt{14} = frac{9-2 sqrt{14} }{2} = frac{7-2 sqrt{7} sqrt{2} +2}{2} = frac{ sqrt{7} ^2-2 sqrt{7} * sqrt{2} + sqrt{2} ^2}{2} =](https://tex.z-dn.net/?f=4%2C5-+sqrt%7B14%7D+%3D+frac%7B9%7D%7B2%7D-+sqrt%7B14%7D+%3D++frac%7B9-2+sqrt%7B14%7D+%7D%7B2%7D+%3D+frac%7B7-2+sqrt%7B7%7D++sqrt%7B2%7D+%2B2%7D%7B2%7D+%3D++frac%7B+sqrt%7B7%7D+%5E2-2+sqrt%7B7%7D+%2A+sqrt%7B2%7D+%2B+sqrt%7B2%7D+%5E2%7D%7B2%7D+%3D+)
![frac{( sqrt{7} - sqrt{2} )^2}{2} frac{( sqrt{7} - sqrt{2} )^2}{2}](https://tex.z-dn.net/?f=+frac%7B%28+sqrt%7B7%7D+-+sqrt%7B2%7D+%29%5E2%7D%7B2%7D+)
4)![frac{( sqrt{7} - sqrt{2} )^2}{2*( sqrt{7} + sqrt{2} )^{-2}} = frac{( sqrt{7} - sqrt{2} )^2*( sqrt{7} + sqrt{2} )^2}{2} = frac{( sqrt{7} ^2- sqrt{2} ^2)^2}{2} = frac{(7-2)^2}{2} = frac{25}{2} =12,5 frac{( sqrt{7} - sqrt{2} )^2}{2*( sqrt{7} + sqrt{2} )^{-2}} = frac{( sqrt{7} - sqrt{2} )^2*( sqrt{7} + sqrt{2} )^2}{2} = frac{( sqrt{7} ^2- sqrt{2} ^2)^2}{2} = frac{(7-2)^2}{2} = frac{25}{2} =12,5](https://tex.z-dn.net/?f=+frac%7B%28+sqrt%7B7%7D+-+sqrt%7B2%7D+%29%5E2%7D%7B2%2A%28+sqrt%7B7%7D+%2B+sqrt%7B2%7D+%29%5E%7B-2%7D%7D+%3D+frac%7B%28+sqrt%7B7%7D+-+sqrt%7B2%7D+%29%5E2%2A%28+sqrt%7B7%7D+%2B+sqrt%7B2%7D+%29%5E2%7D%7B2%7D+%3D+frac%7B%28+sqrt%7B7%7D+%5E2-+sqrt%7B2%7D+%5E2%29%5E2%7D%7B2%7D+%3D+frac%7B%287-2%29%5E2%7D%7B2%7D+%3D+frac%7B25%7D%7B2%7D+%3D12%2C5)
5) 14 - 12,5 = 1,5
Ответ: 1,5
Во втором варианте 4.
1)![sqrt{7+4 sqrt{3} } = sqrt{4+4 sqrt{3} +3} = sqrt{2^2+2*2* sqrt{3} + sqrt{3} ^2} = sqrt{(2+ sqrt{3} )^2} sqrt{7+4 sqrt{3} } = sqrt{4+4 sqrt{3} +3} = sqrt{2^2+2*2* sqrt{3} + sqrt{3} ^2} = sqrt{(2+ sqrt{3} )^2}](https://tex.z-dn.net/?f=+sqrt%7B7%2B4+sqrt%7B3%7D+%7D+%3D++sqrt%7B4%2B4+sqrt%7B3%7D+%2B3%7D+%3D+sqrt%7B2%5E2%2B2%2A2%2A+sqrt%7B3%7D+%2B+sqrt%7B3%7D+%5E2%7D+%3D+sqrt%7B%282%2B+sqrt%7B3%7D+%29%5E2%7D+)
![=2+ sqrt{3} =2+ sqrt{3}](https://tex.z-dn.net/?f=%3D2%2B+sqrt%7B3%7D+)
2) (4-2√3)·(2+√3) = 2·(2-√3)·(2+√3) = 2·(4-3) = 2 · 1 = 2
3)![sqrt{7} -4= frac{2 sqrt{7} -8}{2}= frac{-(1-2 sqrt{7} +7)}{2} = frac{-(1- sqrt{7} )^2}{2} sqrt{7} -4= frac{2 sqrt{7} -8}{2}= frac{-(1-2 sqrt{7} +7)}{2} = frac{-(1- sqrt{7} )^2}{2}](https://tex.z-dn.net/?f=+sqrt%7B7%7D+-4%3D+frac%7B2+sqrt%7B7%7D+-8%7D%7B2%7D%3D+frac%7B-%281-2+sqrt%7B7%7D+%2B7%29%7D%7B2%7D+%3D+frac%7B-%281-+sqrt%7B7%7D+%29%5E2%7D%7B2%7D++)
4)![frac{-(1- sqrt{7} )^2}{2*(1+ sqrt{7} )^{-2}} = frac{-(1- sqrt{7} )^2*(1+ sqrt{7} )^2}{2} = frac{-(1-7)^2}{2}= frac{-36}{2} =-18 frac{-(1- sqrt{7} )^2}{2*(1+ sqrt{7} )^{-2}} = frac{-(1- sqrt{7} )^2*(1+ sqrt{7} )^2}{2} = frac{-(1-7)^2}{2}= frac{-36}{2} =-18](https://tex.z-dn.net/?f=+frac%7B-%281-+sqrt%7B7%7D+%29%5E2%7D%7B2%2A%281%2B+sqrt%7B7%7D+%29%5E%7B-2%7D%7D+%3D+frac%7B-%281-+sqrt%7B7%7D+%29%5E2%2A%281%2B+sqrt%7B7%7D+%29%5E2%7D%7B2%7D+%3D+frac%7B-%281-7%29%5E2%7D%7B2%7D%3D+frac%7B-36%7D%7B2%7D+%3D-18+)
5) 2 - 18 = - 16
Решаю по действиям.
1)
2) (6+2√2)·(3-√2) = 2·(3+√2)·(3-√2) = 2·(3²-√2²) = 2 · (9 - 2) = 2 · 7 = 14
3)
4)
5) 14 - 12,5 = 1,5
Ответ: 1,5
Во втором варианте 4.
1)
2) (4-2√3)·(2+√3) = 2·(2-√3)·(2+√3) = 2·(4-3) = 2 · 1 = 2
3)
4)
5) 2 - 18 = - 16
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