若实数a,b满足条件(a/b)+(b/a)=2,求(a2+ab+b2)/(a2+4ab+b2)的值
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![若实数a,b满足条件(a/b)+(b/a)=2,求(a2+ab+b2)/(a2+4ab+b2)的值](/uploads/image/z/971319-39-9.jpg?t=%E8%8B%A5%E5%AE%9E%E6%95%B0a%2Cb%E6%BB%A1%E8%B6%B3%E6%9D%A1%E4%BB%B6%EF%BC%88a%2Fb%EF%BC%89%2B%EF%BC%88b%2Fa%EF%BC%89%3D2%2C%E6%B1%82%28a2%2Bab%2Bb2%29%2F%28a2%2B4ab%2Bb2%29%E7%9A%84%E5%80%BC)
若实数a,b满足条件(a/b)+(b/a)=2,求(a2+ab+b2)/(a2+4ab+b2)的值
若实数a,b满足条件(a/b)+(b/a)=2,求(a2+ab+b2)/(a2+4ab+b2)的值
若实数a,b满足条件(a/b)+(b/a)=2,求(a2+ab+b2)/(a2+4ab+b2)的值
原式=(a²+ab+b²)/(a²+4ab+b²);分子分母同除以ab得:
=(a/b+1+b/a)/(a/b+4+b/a)
=(2+1)/(2+4)
=1/2;
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