If 5x + 4y = 12 and xy = 2, then find the value of 125x³ + 64y³.

Correct option is A

Given:

5x + 4y = 12

xy = 2

Formula Used:

​$$(a+b)^2 = a^{3} + b^{3} +3ab (a+ b)$$​​

Solution:  

Using the formula:

​$$(5x+4y)^3 = 125x^3 +64y^3 +3(5x)(4y)[5x+4y] \\ \ \\ (12)^3 = 125x^3 +64y^3+60(2)[12] \\ \ \\ 1728= 125x^3 +64y^3 +1440 \\ \ \\ 125x^3 +64y^3 = 1728 - 1440 = 288$$​​

The value of $$125x^3 + 64y^3$$​ is 288