Предмет: Алгебра,
автор: AnteK
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1.059.
![sqrt{ frac{ sqrt{2} }{a}+ frac{a}{ sqrt{2} } +2 }= sqrt{ frac{( sqrt{2})^2 +a^2+2a sqrt{2} }{a sqrt{2} } }= sqrt{ frac{(a+ sqrt{2})^2 }{a sqrt{2} } }= frac{a+ sqrt{2} }{ sqrt{acdot sqrt[4]{2} } }](https://tex.z-dn.net/?f=+sqrt%7B+frac%7B+sqrt%7B2%7D+%7D%7Ba%7D%2B+frac%7Ba%7D%7B+sqrt%7B2%7D+%7D+%2B2+%7D%3D+sqrt%7B+frac%7B%28+sqrt%7B2%7D%29%5E2+%2Ba%5E2%2B2a+sqrt%7B2%7D+%7D%7Ba+sqrt%7B2%7D+%7D+%7D%3D+sqrt%7B+frac%7B%28a%2B+sqrt%7B2%7D%29%5E2+%7D%7Ba+sqrt%7B2%7D+%7D+%7D%3D+frac%7Ba%2B+sqrt%7B2%7D+%7D%7B+sqrt%7Bacdot++sqrt%5B4%5D%7B2%7D+%7D+%7D+%0A "sqrt{ frac{ sqrt{2} }{a}+ frac{a}{ sqrt{2} } +2 }= sqrt{ frac{( sqrt{2})^2 +a^2+2a sqrt{2} }{a sqrt{2} } }= sqrt{ frac{(a+ sqrt{2})^2 }{a sqrt{2} } }= frac{a+ sqrt{2} }{ sqrt{acdot sqrt[4]{2} } }")
![a sqrt{2a}- sqrt[4]{8a^4}= a sqrt{2a}-sqrt[4]{(2 sqrt{2} a^2)^2}=a sqrt{2a}-sqrt{2 sqrt{2} a^2}= \ \ =a sqrt{2}cdot( sqrt{a} - sqrt[4]{2})](https://tex.z-dn.net/?f=a+sqrt%7B2a%7D-+sqrt%5B4%5D%7B8a%5E4%7D%3D+a+sqrt%7B2a%7D-sqrt%5B4%5D%7B%282+sqrt%7B2%7D+a%5E2%29%5E2%7D%3Da+sqrt%7B2a%7D-sqrt%7B2+sqrt%7B2%7D+a%5E2%7D%3D+%5C++%5C+%3Da+sqrt%7B2%7Dcdot%28+sqrt%7Ba%7D+-+sqrt%5B4%5D%7B2%7D%29++++ "a sqrt{2a}- sqrt[4]{8a^4}= a sqrt{2a}-sqrt[4]{(2 sqrt{2} a^2)^2}=a sqrt{2a}-sqrt{2 sqrt{2} a^2}= \ \ =a sqrt{2}cdot( sqrt{a} - sqrt[4]{2})")
![frac{a+ sqrt{2} }{ sqrt{a}cdot sqrt[4]{2} } - frac{a^2 sqrt[4]{2} -2 sqrt{a} }{a sqrt{2}cdot( sqrt{a}- sqrt[4]{2}) } = frac{(a +sqrt{2})( sqrt{a}- sqrt[4]{2})cdot sqrt{a}cdot sqrt[4]{2} -a^2 sqrt[4]{2}+2 sqrt{a}}{a sqrt{2}cdot( sqrt{a}- sqrt[4]{2})}=](https://tex.z-dn.net/?f=+frac%7Ba%2B+sqrt%7B2%7D+%7D%7B+sqrt%7Ba%7Dcdot++sqrt%5B4%5D%7B2%7D++%7D+-+frac%7Ba%5E2+sqrt%5B4%5D%7B2%7D+-2+sqrt%7Ba%7D+%7D%7Ba+sqrt%7B2%7Dcdot%28+sqrt%7Ba%7D-+sqrt%5B4%5D%7B2%7D%29+++%7D+%3D+frac%7B%28a+%2Bsqrt%7B2%7D%29%28+sqrt%7Ba%7D-+sqrt%5B4%5D%7B2%7D%29cdot+sqrt%7Ba%7Dcdot+sqrt%5B4%5D%7B2%7D+-a%5E2+sqrt%5B4%5D%7B2%7D%2B2+sqrt%7Ba%7D%7D%7Ba+sqrt%7B2%7Dcdot%28+sqrt%7Ba%7D-+sqrt%5B4%5D%7B2%7D%29%7D%3D++ "frac{a+ sqrt{2} }{ sqrt{a}cdot sqrt[4]{2} } - frac{a^2 sqrt[4]{2} -2 sqrt{a} }{a sqrt{2}cdot( sqrt{a}- sqrt[4]{2}) } = frac{(a +sqrt{2})( sqrt{a}- sqrt[4]{2})cdot sqrt{a}cdot sqrt[4]{2} -a^2 sqrt[4]{2}+2 sqrt{a}}{a sqrt{2}cdot( sqrt{a}- sqrt[4]{2})}=")
![= frac{a^2 sqrt[4]{2}-a sqrt{a}cdot sqrt{2}+a sqrt{2}cdot sqrt[4]{2}- sqrt{2}cdot sqrt{a}cdot sqrt{2}-a^2 sqrt{2}+2 sqrt{a} }{a sqrt{2}cdot( sqrt{a}- sqrt[4]{2})}= \ \ = frac{-a sqrt{a}cdot sqrt{2}+a sqrt{2}cdot sqrt[4]{2}}{a sqrt{2}cdot( sqrt{a}- sqrt[4]{2})}= frac{ sqrt{a}cdot sqrt{2}( sqrt[4]{2}- sqrt{a})}{a sqrt{2}cdot( sqrt{a} - sqrt[4]{2}) } =-1](https://tex.z-dn.net/?f=%3D+frac%7Ba%5E2+sqrt%5B4%5D%7B2%7D-a+sqrt%7Ba%7Dcdot+sqrt%7B2%7D%2Ba+sqrt%7B2%7Dcdot+sqrt%5B4%5D%7B2%7D-+sqrt%7B2%7Dcdot+sqrt%7Ba%7Dcdot+sqrt%7B2%7D-a%5E2+sqrt%7B2%7D%2B2+sqrt%7Ba%7D++++%7D%7Ba+sqrt%7B2%7Dcdot%28+sqrt%7Ba%7D-+sqrt%5B4%5D%7B2%7D%29%7D%3D++%5C++%5C+%3D+frac%7B-a+sqrt%7Ba%7Dcdot+sqrt%7B2%7D%2Ba+sqrt%7B2%7Dcdot+sqrt%5B4%5D%7B2%7D%7D%7Ba+sqrt%7B2%7Dcdot%28+sqrt%7Ba%7D-+sqrt%5B4%5D%7B2%7D%29%7D%3D+frac%7B+sqrt%7Ba%7Dcdot+sqrt%7B2%7D%28+sqrt%5B4%5D%7B2%7D-+sqrt%7Ba%7D%29%7D%7Ba+sqrt%7B2%7Dcdot%28+sqrt%7Ba%7D+-+sqrt%5B4%5D%7B2%7D%29++%7D+%3D-1 "= frac{a^2 sqrt[4]{2}-a sqrt{a}cdot sqrt{2}+a sqrt{2}cdot sqrt[4]{2}- sqrt{2}cdot sqrt{a}cdot sqrt{2}-a^2 sqrt{2}+2 sqrt{a} }{a sqrt{2}cdot( sqrt{a}- sqrt[4]{2})}= \ \ = frac{-a sqrt{a}cdot sqrt{2}+a sqrt{2}cdot sqrt[4]{2}}{a sqrt{2}cdot( sqrt{a}- sqrt[4]{2})}= frac{ sqrt{a}cdot sqrt{2}( sqrt[4]{2}- sqrt{a})}{a sqrt{2}cdot( sqrt{a} - sqrt[4]{2}) } =-1")
1.058.
1.058.
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