Answer: The given expression is:
m² +........+ 1/m²
We can notice that the expression has an even number of terms, and the first and last term are perfect squares, which suggests that it might be possible to write the expression as the square of a binomial.
Let's try to write the expression in the form of (a + b)²:
(a + b)² = a² + 2ab + b²
If we set a = m and b = 1/m, we get:
(a + b)² = m² + 2(m)(1/m) + (1/m)² = m² + 2 + 1/m²
Comparing this with the given expression, we see that it is the same as the given expression with 2 added to it.
Therefore, to make the given expression a perfect square, we need to add 2 to it.
So, the term to be inserted is 2.
The expression m² +........+ 1/m² can be written as (m + 1/m)² - 2.
Explanation: