Answer 1

We have to find the value `a^2 +b^2`

Given  a-b = 5, ab = 12 

Using identity  `(a - b)^2 = a^2  - 2ab +b^2`

By substituting the value of   a-b = 5 ,ab = 12 we get ,

`(5)^2 = a^2 +b^2 - 2 xx 12`

`5 xx 5 = a^2 +b^2 - 2 xx 12`

`25 = a^2 +b^2 -24`

By transposing – 24 to left hand side we get 

`25 + 24 = a^2 +b^2`

         `49 = a^2 +b^2`

Hence the value of  `a^2 +b^2` is  49.