已知a，b，x，y∈R，证明：（a2+b2）（x2+y2）≥（ax+by）2，并利用上述结论求（m2+4n2）（ 1m2 + 4n2 ）的最小值（其中m，n∈R且m≠0，n≠0）．_刷题宝

题干

已知a，b，x，y∈R，证明：（a²+b²）（x²+y²）≥（ax+by）²，并利用上述结论求（m²+4n²）（

1

m

2

+

4

n

2

）的最小值（其中m，n∈R且m≠0，n≠0）．

上一题下一题 0.0难度选择题更新时间:2018-03-07 07:03:06

答案(点此获取答案解析）

证明：∵b²x²+a²y²≥2abxy，

∴a²x²+b²y²+b²x²+a²y²≥a²x²+b²y²+2abxy，

即（a^2<

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