Given a - b = 2, $$a^3 - b^3 = 26$$ then $$(a + b)^2$$ is

Given : $$a^3 - b^3 = 26$$

Also, $$a-b=2$$

Cubing both sides,

=> $$(a-b)^3=(2)^3$$

=> $$a^3-b^3-3ab(a-b)=8$$

=> $$26-3ab(2)=8$$

=> $$6ab=26-8=18$$

=> $$ab=\frac{18}{6}=3$$ -------------(i)

Also, $$a^3-b^3=(a-b)(a^2+b^2+ab)$$

=> $$26=2(a^2+b^2+3)$$

=> $$a^2+b^2+3=\frac{26}{2}=13$$

=> $$a^2+b^2=13-3=10$$ --------------(ii)

$$\therefore$$ $$(a + b)^2$$ = $$a^2+b^2+2ab$$

Using equations (i) and (ii), we get :

= $$10+2(3)=16$$

=> Ans - (C)