已知x加y等于a,x的平方加y的平方等于b的平方。求x的四次方加y的四次方
x y=ax² y²=b²(x y)²=a²x² 2xy y²=a²2xy=a²-b²(x y)^4=x^4 4yx^3 4xy^3 6x²y² y^4x^4 y^4=(x y)^4-4xy(x² y²)-6x²y² =a^4-2(a²-b²)b²-3/2(a²-b²)² =a^4-2a²b² 2b^4-3/2(a^4-2a²b² b^4) =a^4-2a²b² 2b^4-3/2a^4 3a²b²-3/2b^4 =-1/2a^4 a²b² 1/2b^4。 全部
x y=ax² y²=b²(x y)²=a²x² 2xy y²=a²2xy=a²-b²(x y)^4=x^4 4yx^3 4xy^3 6x²y² y^4x^4 y^4=(x y)^4-4xy(x² y²)-6x²y² =a^4-2(a²-b²)b²-3/2(a²-b²)² =a^4-2a²b² 2b^4-3/2(a^4-2a²b² b^4) =a^4-2a²b² 2b^4-3/2a^4 3a²b²-3/2b^4 =-1/2a^4 a²b² 1/2b^4。
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