The Go Interest Group of Hongxing Primary School has four children and two coaches. The difference between the four children and the two coaches is two years, and the sum of the squares of the six people's ages is 2796. What is the total age of six people?

analyse

The primary school students are between the ages of, so the ages of these four children should be:, and the sum of squares equals:

If the average age of the two coaches is, then the two coaches are,

The sum of the ages of six people is equal to:

(years old)

Refine and improve

The key to solve this problem lies in:

1) The age of primary school students is between years old, which is common sense and an implicit condition of this problem;

2) This question uses the following formula:

This formula is the teaching content of junior high school mathematics. A considerable number of gifted students in grades 5 and 6 have mastered this formula, which can be considered as "transitional knowledge".

The more general form of this formula is as follows:

This is a common formula in college entrance examination mathematics.

This problem is not difficult, but also very interesting, and it is an excellent competition problem.

Finally, the author puts forward some views:

This description in the original question is not good, so it is suggested to delete the word "year" and say directly: the sum of the squares of the ages of six people is 2796.