1, square inequality
Square inequality is to square the variables in sugar water inequality, and use the square root property or square both sides of inequality at the same time to get a new inequality form. Such as inequality x >；; 2 Enter x^2 > 4. Sugar water inequality refers to a common inequality in mathematics, and different forms of inequality can be obtained through transformation.
2. Reciprocal inequality
Reciprocal inequality is to reverse the sign of inequality in syrup inequality, that is, change the greater than sign to the less than sign, and the less than sign to the greater than sign, and take the reciprocal of both sides of inequality. For example, the inequality A >: B is converted into1/a.
3. Triangle inequality
Trigonometric inequality is to bring variables in sugar water inequality into trigonometric function, and use the deformation of trigonometric function to solve inequality. For example, for sine function, we can use monotonicity and periodicity of sine function to deal with inequality. These deformation techniques are very useful in solving mathematical problems and proving mathematical theorems, and can be used flexibly according to specific problems and needs.
Application of sugar water inequality:
1, inequality solution
Sugar water inequality is often used to solve inequality problems in mathematics. Through the transformation and simplification of inequality, we can find the solution set of inequality, that is, the range of variables that meet the inequality conditions. Through the inequality deformation of the function, we can get important information such as monotonicity, zero point and extreme point of the function, so as to draw the image of the function and study its behavior. This is very useful for solving mathematical problems.
2, the maximum problem
Sugar inequality can be used to solve the maximum problem, that is, to find the value of the variable that makes an expression reach the maximum or minimum. The objective function and constraint conditions are combined into inequality, which can be solved by sugar water inequality method, so as to get the position and value of the maximum point.
3. Mathematical proof
Sugar inequality also plays an important role in mathematical proof. Some important mathematical inequalities and theorems, such as Cauchy-Schwartz inequality and mean inequality, can be derived by using the deformation method of sugar inequality, which is widely used in mathematical analysis, probability theory, geometry and other fields.