1. the method of finding algebraic range by undetermined coefficient method

Known m 1

(1) let g(a, b) = PF 1 (a, b)+QF2 (a, b); (2) The undetermined coefficients p and q are obtained by constant deformation; (3) The range of g (a, b) can be obtained according to the same additivity of inequality.

2. The method of comparing the sizes of two numbers (formulas)

3. Steps to solve a quadratic inequality with parameters.

① If the quadratic term contains parameters, discuss whether the parameters are equal to 0, less than 0 or greater than 0, and then transform the inequality into a linear inequality or a quadratic inequality with positive quadratic coefficient;

(2) Judging the number of real roots of the equation corresponding to the unary quadratic inequality, that is, discussing the relationship between the discriminant δ and 0;

③ When it is determined that the equation has no real roots or two identical real roots, the solution set can be written directly; When an equation has two different real roots, the relationship between the two real roots should be discussed to determine the solution set.

4. Methods and steps to solve quadratic inequality in one variable.

5. Find the maximum value by elimination method

The elimination method is to establish the functional relationship between two quantities according to conditions, and then substitute it into an algebraic expression to find the maximum value of the function. Sometimes there will be multiple problems, and the solution is to use basic inequalities to eliminate and solve them. However, care should be taken to keep the range of elements.