A,B,C大于0,且A(A+B+C)+BC=4-2更号3,则2A+B+C的最小直是多少?
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![A,B,C大于0,且A(A+B+C)+BC=4-2更号3,则2A+B+C的最小直是多少?](/uploads/image/z/5639642-26-2.jpg?t=A%2CB%2CC%E5%A4%A7%E4%BA%8E0%2C%E4%B8%94A%EF%BC%88A%2BB%2BC%EF%BC%89%2BBC%3D4-2%E6%9B%B4%E5%8F%B73%2C%E5%88%992A%2BB%2BC%E7%9A%84%E6%9C%80%E5%B0%8F%E7%9B%B4%E6%98%AF%E5%A4%9A%E5%B0%91%3F)
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A,B,C大于0,且A(A+B+C)+BC=4-2更号3,则2A+B+C的最小直是多少?
A,B,C大于0,且A(A+B+C)+BC=4-2更号3,则2A+B+C的最小直是多少?
A,B,C大于0,且A(A+B+C)+BC=4-2更号3,则2A+B+C的最小直是多少?
BC <= (B+C)^2 / 4
设
X=2A+B+C
=>
BC <=(X-2A)^2/4 =XX/4 -AX +AA
=>
A(A+B+C)+BC
<=
A(X-A) + XX/4 -A(X-A) = XX/4
=>
4-2√3 <= XX/4
=>
√3-1 <= X/2
=>
X最小值2√3-2