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1 способ:
![(sqrt[3]{a}+sqrt[3]{b})^2-(sqrt[3]{a}-sqrt[3]{b})^2=\\=; ; [; A^2-B^2=(A-B)cdot (A+B)]=\\=((sqrt[3]{a}+sqrt[3]{b})-(sqrt[3]{a}-sqrt[3]{b}))cdot ((sqrt[3]{a}+sqrt[3]{b})+(sqrt[3]{a}-sqrt[3]{b}))=\\=2sqrt[3]{b}cdot 2sqrt[3]{a}=4sqrt[3]{ab}](https://tex.z-dn.net/?f=%28sqrt%5B3%5D%7Ba%7D%2Bsqrt%5B3%5D%7Bb%7D%29%5E2-%28sqrt%5B3%5D%7Ba%7D-sqrt%5B3%5D%7Bb%7D%29%5E2%3D%5C%5C%3D%3B+%3B+%5B%3B+A%5E2-B%5E2%3D%28A-B%29cdot+%28A%2BB%29%5D%3D%5C%5C%3D%28%28sqrt%5B3%5D%7Ba%7D%2Bsqrt%5B3%5D%7Bb%7D%29-%28sqrt%5B3%5D%7Ba%7D-sqrt%5B3%5D%7Bb%7D%29%29cdot+%28%28sqrt%5B3%5D%7Ba%7D%2Bsqrt%5B3%5D%7Bb%7D%29%2B%28sqrt%5B3%5D%7Ba%7D-sqrt%5B3%5D%7Bb%7D%29%29%3D%5C%5C%3D2sqrt%5B3%5D%7Bb%7Dcdot+2sqrt%5B3%5D%7Ba%7D%3D4sqrt%5B3%5D%7Bab%7D "(sqrt[3]{a}+sqrt[3]{b})^2-(sqrt[3]{a}-sqrt[3]{b})^2=\\=; ; [; A^2-B^2=(A-B)cdot (A+B)]=\\=((sqrt[3]{a}+sqrt[3]{b})-(sqrt[3]{a}-sqrt[3]{b}))cdot ((sqrt[3]{a}+sqrt[3]{b})+(sqrt[3]{a}-sqrt[3]{b}))=\\=2sqrt[3]{b}cdot 2sqrt[3]{a}=4sqrt[3]{ab}")
2способ:
![(sqrt[3]{a}+sqrt[3]{b})^2-(sqrt[3]{a}-sqrt[3]{b})^2=\\=; ; [, (Apm B)^2=A^2pm 2AB+B^2, ]=\\=sqrt[3]{a^2}+2sqrt[3]{a}sqrt[3]{b}+sqrt[3]{b^2}-(sqrt[3]{a^2}-2sqrt[3]{a}sqrt[3]{b}+sqrt[3]{b})=\\=2sqrt[3]{a}sqrt[3]{b}+2sqrt[3]{a}sqrt[3]{b}=4sqrt[3]{ab}](https://tex.z-dn.net/?f=%28sqrt%5B3%5D%7Ba%7D%2Bsqrt%5B3%5D%7Bb%7D%29%5E2-%28sqrt%5B3%5D%7Ba%7D-sqrt%5B3%5D%7Bb%7D%29%5E2%3D%5C%5C%3D%3B+%3B+%5B%2C+%28Apm+B%29%5E2%3DA%5E2pm+2AB%2BB%5E2%2C+%5D%3D%5C%5C%3Dsqrt%5B3%5D%7Ba%5E2%7D%2B2sqrt%5B3%5D%7Ba%7Dsqrt%5B3%5D%7Bb%7D%2Bsqrt%5B3%5D%7Bb%5E2%7D-%28sqrt%5B3%5D%7Ba%5E2%7D-2sqrt%5B3%5D%7Ba%7Dsqrt%5B3%5D%7Bb%7D%2Bsqrt%5B3%5D%7Bb%7D%29%3D%5C%5C%3D2sqrt%5B3%5D%7Ba%7Dsqrt%5B3%5D%7Bb%7D%2B2sqrt%5B3%5D%7Ba%7Dsqrt%5B3%5D%7Bb%7D%3D4sqrt%5B3%5D%7Bab%7D "(sqrt[3]{a}+sqrt[3]{b})^2-(sqrt[3]{a}-sqrt[3]{b})^2=\\=; ; [, (Apm B)^2=A^2pm 2AB+B^2, ]=\\=sqrt[3]{a^2}+2sqrt[3]{a}sqrt[3]{b}+sqrt[3]{b^2}-(sqrt[3]{a^2}-2sqrt[3]{a}sqrt[3]{b}+sqrt[3]{b})=\\=2sqrt[3]{a}sqrt[3]{b}+2sqrt[3]{a}sqrt[3]{b}=4sqrt[3]{ab}")
2способ:
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http://znanija.com/task/13308267
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