Inequalities have three special properties:
(1) Inequality 1: both sides of the inequality add (or subtract) the same number (or formula) at the same time, and the direction of the inequality remains unchanged;
2 Inequality 2: Both sides of the inequality are multiplied (or divided) by the same positive number at the same time, and the direction of the inequality remains unchanged;
3 Inequality 3: Both sides of the inequality are multiplied (or divided) by the same negative number at the same time, and the direction of the inequality changes. ? Summary: when the product of two positive numbers is constant, their sum has a minimum value; When the sum of two positive numbers is constant, their product has a maximum value.
Extended data
Theorem formula
The solution to inequality is to use the properties of functions. The unreasonable inequality of the opposite side is transformed into a rational inequality.
From high order to low order, step-by-step transformation should be equivalent. The mutual transformation between numbers and shapes helps to solve problems.
The method of proving inequality is powerful in real number property. Difference is compared with 0, and quotient is compared with 1.
Comprehensive method with good direct difficulty analysis and clear thinking. Non-negative common basic expressions, positive difficulties are reduced to absurdity.
There are also important inequalities and mathematical induction. Graphic function help, drawing, modeling, construction methods.