review calculus 3, try to solve the following two examples:
Example 1: solve max (x^1 x^2 )under the condition x^1 +x^2=1
Example 2: solve max( x^1 x^2+x^2 x^3 +x^3 x^1) under the condition X^1+ x^2+x^3=1
Using Lagrange multiplier in calculus 3. write some Definitions and Theories and examples