若b/a+a/b=2,则a²+2ab+b²/a²+4ab+b²的值
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若b/a+a/b=2,则a²+2ab+b²/a²+4ab+b²的值
![若b/a+a/b=2,则a²+2ab+b²/a²+4ab+b²的值](/uploads/image/z/20264670-54-0.jpg?t=%E8%8B%A5b%2Fa%2Ba%2Fb%3D2%2C%E5%88%99a%26%23178%3B%2B2ab%2Bb%26%23178%3B%2Fa%26%23178%3B%2B4ab%2Bb%26%23178%3B%E7%9A%84%E5%80%BC)
/a+a/b=2
b²/ab+a²/ab=2
a²+b²=2ab
a²+2ab+b²/a²+4ab+b²
=[(a²+b²)+2ab]/[(a²+b²)+4ab]
=(2ab+2ab)/(2ab+4ab)
=4ab/6ab
=2/3
b²/ab+a²/ab=2
a²+b²=2ab
a²+2ab+b²/a²+4ab+b²
=[(a²+b²)+2ab]/[(a²+b²)+4ab]
=(2ab+2ab)/(2ab+4ab)
=4ab/6ab
=2/3
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