Câu hỏi của Nguyễn Võ Anh Nguyên

Question

Tìm Min:

$N=x+2y-\sqrt{2x-1}-5\sqrt{4y-3}+13$

Mog mn giúp vs ạ

alibaba nguyễn · Accepted Answer

$N=x+2y-\sqrt{2x-1}-5\sqrt{4y-3}+13$

$2N=2x+4y-2\sqrt{2x-1}-10\sqrt{4y-3}+26$

$=\left(2x-1-2\sqrt{2x-1}+1\right)+\left(4y-3-10\sqrt{4y-3}+25\right)+4$

$=\left(\sqrt{2x-1}-1\right)^2+\left(\sqrt{4y-3}-5\right)^2+4\ge4$

Câu trả lời:

$N=x+2y-\sqrt{2x-1}-5\sqrt{4y-3}+13$

$2N=2x+4y-2\sqrt{2x-1}-10\sqrt{4y-3}+26$

$=\left(2x-1-2\sqrt{2x-1}+1\right)+\left(4y-3-10\sqrt{4y-3}+25\right)+4$

$=\left(\sqrt{2x-1}-1\right)^2+\left(\sqrt{4y-3}-5\right)^2+4\ge4$