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4) =![sqrt{ frac{(2,87-1,97)(2,87+1,97)}{(4,37-3,47)(4,37+3,47)} } = sqrt{ frac{0,9*4,84}{0,9*7,84} }= sqrt{ frac{484}{784} }= frac{22}{28}= frac{11}{14} sqrt{ frac{(2,87-1,97)(2,87+1,97)}{(4,37-3,47)(4,37+3,47)} } = sqrt{ frac{0,9*4,84}{0,9*7,84} }= sqrt{ frac{484}{784} }= frac{22}{28}= frac{11}{14}](https://tex.z-dn.net/?f=+sqrt%7B+frac%7B%282%2C87-1%2C97%29%282%2C87%2B1%2C97%29%7D%7B%284%2C37-3%2C47%29%284%2C37%2B3%2C47%29%7D+%7D+%3D+sqrt%7B+frac%7B0%2C9%2A4%2C84%7D%7B0%2C9%2A7%2C84%7D+%7D%3D+sqrt%7B+frac%7B484%7D%7B784%7D+%7D%3D++frac%7B22%7D%7B28%7D%3D+frac%7B11%7D%7B14%7D++++)
№341
2) =![sqrt{( sqrt{7})^2-2*2 sqrt{7}+2^2 }= sqrt{( sqrt{7}-2)^2 }= sqrt{7}-2 sqrt{( sqrt{7})^2-2*2 sqrt{7}+2^2 }= sqrt{( sqrt{7}-2)^2 }= sqrt{7}-2](https://tex.z-dn.net/?f=+sqrt%7B%28+sqrt%7B7%7D%29%5E2-2%2A2+sqrt%7B7%7D%2B2%5E2+%7D%3D+sqrt%7B%28+sqrt%7B7%7D-2%29%5E2+%7D%3D+sqrt%7B7%7D-2+++)
=![sqrt{( sqrt{7})^2-2*3 sqrt{7}+3^2 }= sqrt{( sqrt{7}-3)^2 } =3- sqrt{7} sqrt{( sqrt{7})^2-2*3 sqrt{7}+3^2 }= sqrt{( sqrt{7}-3)^2 } =3- sqrt{7}](https://tex.z-dn.net/?f=+sqrt%7B%28+sqrt%7B7%7D%29%5E2-2%2A3+sqrt%7B7%7D%2B3%5E2++%7D%3D+sqrt%7B%28+sqrt%7B7%7D-3%29%5E2+%7D+%3D3-+sqrt%7B7%7D++)
![sqrt{7}-2+3- sqrt{7} =1 sqrt{7}-2+3- sqrt{7} =1](https://tex.z-dn.net/?f=+sqrt%7B7%7D-2%2B3-+sqrt%7B7%7D+%3D1+)
4)6-√20=6-2√5=(√5)²-2√5+1²=(√5-1)²
6+√20=6+2√5=(√5)²+2√5+1²=(√5+1)²
![frac{1}{ sqrt{5}-1+1 }- frac{1}{ sqrt{5}+1-1 } = frac{1}{ sqrt{5} }- frac{1}{ sqrt{5} }=0 frac{1}{ sqrt{5}-1+1 }- frac{1}{ sqrt{5}+1-1 } = frac{1}{ sqrt{5} }- frac{1}{ sqrt{5} }=0](https://tex.z-dn.net/?f=+frac%7B1%7D%7B+sqrt%7B5%7D-1%2B1+%7D-+frac%7B1%7D%7B+sqrt%7B5%7D%2B1-1+%7D+%3D+frac%7B1%7D%7B+sqrt%7B5%7D+%7D-+frac%7B1%7D%7B+sqrt%7B5%7D+%7D%3D0++++)
№341
2) =
=
4)6-√20=6-2√5=(√5)²-2√5+1²=(√5-1)²
6+√20=6+2√5=(√5)²+2√5+1²=(√5+1)²
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