SSC CGL 2022 PYQ — Question 57

The correct answer is option 3 i.e. 19

We have given, 2$\sqrt{2}$x³ - 3$\sqrt{3}$y³ = ($\sqrt{2}x-\sqrt{3}y$)(Ax² - Bxy + Cy²)........(1)

We know that a³ - b³ = (a - b) (a² + ab + b²)

So,  2$\sqrt{2}$x³ - 3$\sqrt{3}$y³ =  ($\sqrt{2}x-\sqrt{3}y$) (2x² + $\sqrt{6}$xy + 3y²)..........(2).

Comparing eq 1 and eq 2

A = 2

B = -$\sqrt{6}$

C = 3 

So, the value of (A² + B² + C²) = (2² + ( -$\sqrt{6}$)² + 3²) = 19