If $(40\sqrt{5}x^3 - 2\sqrt{2}y^3) ÷ (2\sqrt{5}x - \sqrt{2}y) = Ax^2 + By^2 - Cxy, $ then find the value of A + 3B - $\sqrt{10}C.$

46

If $(40\sqrt{5}x^3 - 2\sqrt{2}y^3) ÷ (2\sqrt{5}x - \sqrt{2}y) = Ax^2 + By^2 - Cxy, $ then find the value of A + 3B - $\sqrt{10}C.$

We know that,

a³ – b³ = (a – b)(a² + b² + ab)

 (40√5x³ – 2√2y³) = [(2√5x – √2y)(2√5x)² + (√2y)² + 2√5 × √2]/(2√5x – √2y)

= (2√5x)² + (√2y)² + 2√5 × √2

= 20x² + 2y² + 2√10xy 

Now,

Comparing all of them we get,

A = 20, B = 2 and C = -2√10

Now,

The value of A + 3B – √10C = (20 + 3 × 2 + 2√10 × √10)

= (20 + 6 + 20) = 46