x/(3^3+4^3)+y/(3^3+6^3)=1 x/(5^3+4^3)+y/(5^3+6^3)=1 求证x+y=43
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x/(3^3+4^3)+y/(3^3+6^3)=1 x/(5^3+4^3)+y/(5^3+6^3)=1 求证x+y=432 不得用三角函数!
【1】去分母,得:(3^3+6^3)x+(3^3+4^3)y=(3^3+4^3)(3^3+6^3),且(5^3+6^3)x+(5^3+4^3)y=(5^3+6^3)(5^3+4^3).两式相减,得:(5^3-3^3)x+(5^3-3^3)y=(4^3+5^3+6^3)5^3-(3^3+4^3+6^3)3^3.【2】(x+y)=[(4^3+5^3+6^3)5^3-(3^3+4^3+6^3)3^3]/(5^3-3^3)=432.
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