Question

Tim GTNN cua bieu thuc:

C=\(\frac{-2}{\left|x+4\right|+\left(y-1.3\right)^{104}+18}\)

Answer 1

Ta có :

\(C=-\frac{2}{\left|x+4\right|+\left(y-1.3\right)^{104}+18}\)

Ta có : | x + 4 | \(\ge\)0 ; ( y - 1.3 )¹⁰⁴ \(\ge\)0 

\(\Rightarrow\) | x + 4 |  + ( y - 1.3 )¹⁰⁴ \(\ge\)0​​​​

\(\Rightarrow\)| x + 4 |  + ( y - 1.3 )¹⁰⁴ ​+ 18 \(\ge\)18

Dấu " = " xảy ra khi \(\hept{\begin{cases}x=0\\y=0\end{cases}}\)

\(\Rightarrow\frac{2}{\left|x+4\right|+\left(y-1.3\right)^{104}+18}\le\frac{2}{18}=\frac{1}{9}\)

\(\Rightarrow\)GTLN của ​\(\frac{2}{\left|x+4\right|+\left(y-1.3\right)^{104}+18}\)là \(\frac{1}{9}\)

\(\Rightarrow\)\(-\frac{2}{\left|x+4\right|+\left(y-1.3\right)^{104}+18}\)có GTNN của ​\(\frac{1}{9}\)

Vậy C_min = \(\frac{1}{9}\)khi \(\hept{\begin{cases}x=0\\y=0\end{cases}}\)

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