Question

若正数a,b,c满足a^2十2ab十4bc十2ca=16求证a十b十c≥4

Answer 1

(b+c)^2≥0

b^2+2bc+c^2≥0

a^2+2ab+2ca+2bc+b^2+2bc+c^2=a^2+2ab+4bc+2ca+b^2+c^2=(a+b+c)^2≥16=4^2(由已知式)

a+b+c≥4(由已知正数a,b,c)

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