Property 6
- For finding the maximum value of the multiplication of the numbers with a fixed sum, the numbers are selected so that their difference is the minimum value possible. For finding the minimum value of the multiplication, the numbers are selected so that their difference is the maximum value possible.
- For finding the maximum value of the addition of numbers with a fixed product, the numbers are selected so that their difference is the maximum value possible. For finding the minimum value of the addition, the numbers are selected so that their difference is the minimum value possible.
- The type of the number is taken into account when selecting the numbers.
1.
\(a,b\in\mathbb{Z}^{+}\)
\(a+b=7\)
\(\Rightarrow \max(a\cdot b)=?\)
2.
\(a,b\in\mathbb{Z}^{+}\)
\(a+b=21\)
\(\Rightarrow \max(a\cdot b)=?\)
3.
\(a,b\in\mathbb{Z}^{+}\)
\(a+b=21\)
\(\Rightarrow \min(a\cdot b)=?\)
4.
\(a,b\in\mathbb{Z}\)
\(a+b=-17\)
\(\Rightarrow \max(a\cdot b)=?\)
5.
\(a,b\in\mathbb{Z}^{-}\)
\(a+b=-11\)
\(\Rightarrow \min(a\cdot b)=?\)
6.
\(a,b\in\mathbb{Z}^{-}\)
\(a+b=-13\)
\(\Rightarrow \max(a\cdot b)=?\)
7.
\(a,b\in\mathbb{Z}^{-}\)
\(a+b=-20\)
\(\Rightarrow \max(a\cdot b)=?\)
8.
\(a,b\in\mathbb{Z}^{+}\)
\(a\cdot b=42\)
\(\Rightarrow \min(a+b)=?\)
9.
\(a,b\in\mathbb{Z}^{+}\)
\(a\cdot b=40\)
\(\Rightarrow \min(a+b)=?\)
10.
\(a,b\in\mathbb{Z}^{+}\)
\(a\cdot b=72\)
\(\Rightarrow \max(a+b)=?\)
11.
\(a,b\in\mathbb{Z}\)
\(a\cdot b=56\)
\(\Rightarrow \max(a+b)=?\)
12.
\(a,b\in\mathbb{Z}\)
\(a\cdot b=56\)
\(\Rightarrow \min(a+b)=?\)
13.
\(a,b\in\mathbb{Z}^{-}\)
\(a\cdot b=30\)
\(\Rightarrow \max(a+b)=?\)