a2/3+b 2/3=4 x=a+3a1/3b2/3 y=b+3a2/3b1/3 求（x+y)2/3+(x-y)2/3 注：所有的分数都为指数
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x+y=a+3a^(1/3)b^(2/3) +b+3a^(2/3)b(1/3)
=(a^1/3)�0�6＋3a^(2/3)b(1/3)＋3a^(1/3)b^(2/3)＋(b^1/3)�0�6
＝（a^1/3+b^1/3）�0�6
∴（x+y）^(2/3)＝〔（a^1/3+b^1/3）�0�6〕^2/3=（a^1/3+b^1/3）�0�5
＝a^(2/3)+2a^(1/3)b^(1/3)+b^(2/3)
=4+2a^(1/3)b^(1/3)
x-y=a+3a^(1/3)b^(2/3) -b-3a^(2/3)b(1/3)
=(a^1/3)�0�6-3a^(2/3)b(1/3)＋3a^(1/3)b^(2/3)-(b^1/3)�0�6
＝（a^1/3-b^1/3）�0�6
∴（x-y）^(2/3)＝〔（a^1/3-b^1/3）�0�6〕^2/3=（a^1/3-b^1/3）�0�5
＝a^(2/3)-2a^(1/3)b^(1/3)+b^(2/3)
＝4－2a^(1/3)b^(1/3)
∴（x+y）^(2/3)+(x-y)^(2/3)＝4+2a^(1/3)b^(1/3)＋4－2a^(1/3)b^(1/3)＝8
=(a^1/3)�0�6＋3a^(2/3)b(1/3)＋3a^(1/3)b^(2/3)＋(b^1/3)�0�6
＝（a^1/3+b^1/3）�0�6
∴（x+y）^(2/3)＝〔（a^1/3+b^1/3）�0�6〕^2/3=（a^1/3+b^1/3）�0�5
＝a^(2/3)+2a^(1/3)b^(1/3)+b^(2/3)
=4+2a^(1/3)b^(1/3)
x-y=a+3a^(1/3)b^(2/3) -b-3a^(2/3)b(1/3)
=(a^1/3)�0�6-3a^(2/3)b(1/3)＋3a^(1/3)b^(2/3)-(b^1/3)�0�6
＝（a^1/3-b^1/3）�0�6
∴（x-y）^(2/3)＝〔（a^1/3-b^1/3）�0�6〕^2/3=（a^1/3-b^1/3）�0�5
＝a^(2/3)-2a^(1/3)b^(1/3)+b^(2/3)
＝4－2a^(1/3)b^(1/3)
∴（x+y）^(2/3)+(x-y)^(2/3)＝4+2a^(1/3)b^(1/3)＋4－2a^(1/3)b^(1/3)＝8
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