Question

Tìm x, y thỏa mãn :

a, 2007\(\left|2x-y\right|\)²⁰⁰⁸ ​+ 2008\(\left|y-4\right|\)²⁰⁰⁷ \(\le\)0

b, \(\left|5x+1\right|+\left|6y-8\right|\le0\)

Answer 1

a)Với mọi \(x;y\in R\) ta có: \(2017\left|2x-y\right|^{2008}+2008\left|y-4\right|^{2007}\ge0\)

mà \(2007\left|2x-y\right|^{2008}+2008\left|y-4\right|^{2007}\le0\)

\(\Rightarrow2007\left|2x-y\right|^{2008}+2008\left|y-4\right|^{2007}=0\)

Dấu "=" xảy ra khi: \(\left\{{}\begin{matrix}x=2\\y=4\end{matrix}\right.\)

b) Với mọi \(x;y\in R\) ta có: \(\left|5x+1\right|+\left|6y-8\right|\ge0\)

mà \(\left|5x+1\right|+\left|6y-8\right|\le0\)

\(\Rightarrow\left|5x+1\right|+\left|6y-8\right|=0\)

Dấu "=" xảy ra khi: \(\left\{{}\begin{matrix}x=-\dfrac{1}{5}\\y=\dfrac{4}{3}\end{matrix}\right.\)