If a + b = 7 and ab = 12 then find the value of a² – ab + b².

Given a + b = 7 and ab = 12

To find: a² – ab + b²

Using formula:

(a + b)² = a² + b² + 2ab

Substituting the value of a + b = 7 and ab = 12 in the formula

We have, 7² = a² + b² + 2×12

49 = a² + b² + 24

a² + b² = 25

Substituting the value of a² + b² = 25 and ab = 12

a² + b² – ab = 25 – 12 = 13