Question

Given that (m + n)² = 12.25 and mn = 1.5, find the value of m² +n².​

Answer 1

9.25

Explanation:

The following expansion will be applied:

`(a + b)^(2) = a^(2) + 2ab + b^(2)`

Applying the above concept to:

`(m + n)^(2) = m^(2) + 2mn + n^(2)`

Rearranging:

`(m + n)^(2)` =
`m^(2) + n^(2) + 2mn`

Substituting the provided values and isolating the expression
`m^(2) + n^(2)`:

`12.25 =m^(2) + n^(2) + 2(1.5)`

`12.25 = m^(2) + n^(2) + 3`

∴
`m^(2) + n^(2) = 12.25 - 3`

= 9.25