Correct Answer - Option 1 : 45

**Given **

a - b = 3

a^{3} - b^{3} = 189

**Formula used**

a^{3} - b^{3} = (a - b) (a^{2}+ ab + b^{2}) ----(1)

(a - b)^{3} = a^{3} - b^{3} - 3ab(a- b) ----(2)

**Calculation**

Using (2)

3³ = 189 - 3ab(3)

27 = 189 - 9ab

⇒ ab = 18

Substituting ab = 18 in (1)

189 = 3(a^{2} + b^{2} + 18)

⇒ a^{2} + b^{2} = 45

∴ a^{2} + b^{2} = 45