- #1
Albert1
- 1,221
- 0
$given :\,\,$ $a,b,c\geq1$
$prove:$
$(1+a)(1+b)(1+c)\geq 2(1+a+b+c)$
$prove:$
$(1+a)(1+b)(1+c)\geq 2(1+a+b+c)$
In mathematics, inequality is a relation between two values, indicating that one value is greater than, less than, or not equal to the other value. This can be represented using symbols such as <, >, ≤, ≥, or ≠.
To prove an inequality, we can use techniques such as induction, contradiction, and mathematical manipulation. We can also use known theorems and properties to simplify the inequality and make it easier to prove.
Proving inequalities is important because it allows us to establish relationships between different values and make comparisons. It also helps us to solve problems and make predictions in various mathematical fields such as calculus, algebra, and geometry.
Some common mistakes to avoid when proving inequalities include incorrect use of symbols, skipping steps in the proof, and making assumptions without proper justification. It is important to carefully follow the rules of mathematical logic and provide clear and logical explanations for each step in the proof.
Inequalities can be proven using both mathematical and real-life examples. In mathematics, we use abstract symbols to represent numbers and relationships, but these concepts can also be applied to real-life situations. For example, we can use inequalities to compare the heights of different buildings or the prices of different products.