Question

The sum of 2 integers is 7 and the sum of their squares is 37 what is the integers

Answer 1

`1` and
`6`.

Explanation:

Let
`x` denote one of the integers. Since the two integers add up to
`7`, the other integer would be
`(7 - x)`.

The sum of the squares of these integers is
`37`. In other words:

`x^(2) + (7 - x)^(2) = 37`.

Expand
`(7 - x)^(2)` using binomial expansion. Simplify and rewrite this equation and solve for
`x`.

`2\, x^(2) - 14\, x + 12 = 0`.

`x^(2) - 7\, x + 6 = 0`.

Using the quadratic formula or factorization,
`x = 1` or
`x = 6`. Thus, the two integers are
`1` and
`6`.