证明：∵(x+y)²=x²+2xy+y²=(y²+xy)+(x²+xy)∴由题设及柯西不等式,可得：[(y²+xy)+(x²+xy)]×{[x²/(y²+xy)]+[y²/(x²+xy)]}≥(x+y)²两边同除以（x+y)
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