If $$x + y = 14; x^3 + y^3 = 1064$$, then the value of $$(x - y)^2$$ is:

Given, $$x + y = 14$$

$$x^3 + y^3 = 1064$$

$$=$$>  $$\left(x+y\right)\left(x^2+y^2-xy\right)=1064$$

$$=$$>  $$14\left(x^2+y^2+2xy-3xy\right)=1064$$

$$=$$>  $$\left(x+y\right)^2-3xy=76$$

$$=$$>  $$\left(14\right)^2-3xy=76$$

$$=$$>  $$196-3xy=76$$

$$=$$>  $$3xy=120$$

$$=$$>  $$xy=40$$

$$\therefore\ $$ $$(x - y)^2=x^2+y^2-2xy$$

$$=x^2+y^2+2xy-4xy$$

$$=\left(x+y\right)^2-4xy$$

$$=\left(14\right)^2-4\left(40\right)$$

$$=196-160$$

$$=36$$

Hence, the correct answer is Option A