Inequalities Mathematical Formulas
One of the most important topic in Competitive math is Inequalities Mathematical Formulas. Few questions will definitely come from this topic.
The sign shows that it is a greater than suppose 5 > 3 which means 5 is bigger than 3.
Ex. 5>4, 9> 7
The sign shows that it is a lesser than suppose 3 < 5 which means 3 is lesser than 5.
Ex. 4<9, 7<9
The sign ≥ shows that both are equal also a is greater than b suppose a≥b .
Ex. a > b
The sign ≤ shows that both are equal also a is lesser than b suppose a≤b ..
Ex.a<b
Types of Inequalities :
- a ≤ b => -a≥b
- a ≤ b => a ± c ≤ b ± c
- a ≤ b, c > 0 => ac ≤ bc, a / c ≤ b / c;
a ≤ b , c < 0 => ac ≥ bc, a / c ≥ b / c
- 0 < a < b ⇒ 1 / a > 1 / b > 0
- a < b < 0 ⇒ 0 > 1 / a > 1 / b
- a < 0 < b ⇒ 1 / a < 0 < 1 / b
- a ≤ b ⇔ an ≤ bn, (n,a,b > 0)
- a ≤ b ⇔ a-n ≤ b-n
- a ≤ b ⇔ In a ≤ In b
- ex ≥ 1 + x
- xx ≥ (1/e)1/e, x ≥ 1
- Xxx ≥ x x ≥ 1
- aa + bb ≥ ab + ba > 1, a , b > 0
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