Question

1) Tìm GTNN:

a)\(C=\frac{4}{5}+\) \(\frac{20}{|3x+5|+|4y+5|+8}\)

b)\(E=\frac{2}{3}+\) \(\frac{21}{\left(x+3y\right)^2+5|x+5|+14}\)

2) Tìm GTLN: 

a)\(A=5+\) \(\frac{-8}{4|5x+7|+24}\)

b)\(B=\frac{6}{5}-\) \(\frac{14}{5|6y-8|+35}\)

Answer 1

1) Chỉ tìm được Max thôi nhé

a) \(C=\frac{4}{5}+\frac{20}{\left|3x+5\right|+\left|4y+5\right|+8}\le\frac{4}{5}+\frac{20}{8}=\frac{33}{10}\left(\forall x,y\right)\)

Dấu "=" xảy ra khi: \(\hept{\begin{cases}\left|3x+5\right|=0\\\left|4y+5\right|=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-\frac{5}{3}\\y=-\frac{5}{4}\end{cases}}\)

b) \(E=\frac{2}{3}+\frac{21}{\left(x+3y\right)^2+5\left|x+5\right|+14}\le\frac{2}{3}+\frac{21}{14}=\frac{13}{6}\left(\forall x,y\right)\)

Dấu "=" xảy ra khi: \(\hept{\begin{cases}\left(x+3y\right)^2=0\\5\left|x+5\right|=0\end{cases}}\Rightarrow\hept{\begin{cases}x=-5\\y=\frac{5}{3}\end{cases}}\)

Answer 2

2) Thì chỉ tìm được GTNN thôi nhé

a) \(A=5+\frac{-8}{4\left|5x+7\right|+24}\ge5-\frac{8}{24}=\frac{14}{3}\left(\forall x\right)\)

Dấu "=" xảy ra khi: \(4\left|5x+7\right|=0\Rightarrow x=-\frac{7}{5}\)

Vậy Min(A) = 14/3 khi x = -7/5

b) \(B=\frac{6}{5}-\frac{14}{5\left|6y-8\right|+35}\ge\frac{6}{5}-\frac{14}{35}=\frac{4}{5}\left(\forall y\right)\)

Dấu "=" xảy ra khi: \(5\left|6y-8\right|=0\Rightarrow x=\frac{4}{3}\)

Vậy Min(B)  = 4/5 khi x = 4/3