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Lightning Farron 01/01/2018 at 21:28By Cauchy-Schwarz's ineq:
\(VP=\dfrac{4a^2}{2ab+2ac}+\dfrac{4b^2}{2ab+2bc}+\dfrac{4c^2}{2ac+2bc}\)
\(\ge\dfrac{\left(2a+2b+2c\right)^2}{4\left(a+b+c\right)}=\dfrac{4\left(a+b+c\right)^2}{4\left(a+b+c\right)}=a+b+c=VT\)
When \(a=b=c=1 \Rightarrow A=3\)
Alone selected this answer. -
FA Liên Quân Garena 08/01/2018 at 21:58By Cauchy-Schwarz's ineq:
VP=4a22ab+2ac+4b22ab+2bc+4c22ac+2bc
≥(2a+2b+2c)24(a+b+c)=4(a+b+c)24(a+b+c)=a+b+c=VT
When a=b=c=1⇒A=3