If 2\(\sqrt {2}{x}^{3}\) - 3\(\sqrt {3}{y}^{3}\) = (\(\sqrt {2}x\) - \(\sqrt {3}y\)) (Ax² + By² + Cxy)

find the value of (A² + B² + C²)

19

⇒ a³  - b³ = (a-b) (a² + b² + ab)

⇒ 2\(\sqrt {2}{x}^{3}\) - 3\(\sqrt {3}{y}^{3}\) = (\(\sqrt {2}x\) - \(\sqrt {3}y\)) (Ax² + By² + Cxy)     ............(i)

⇒  (\(\sqrt {2}{x})^{3}\) - (\(\sqrt {3}{y})^{3}\) = (\(\sqrt {2}x\) - \(\sqrt {3}y\)) ((\(\sqrt {2}\)x)² + (\(\sqrt {3}\)y)² + \(\sqrt {3×2}\)xy) ........(ii)

Comparing (i) and (ii)

So, A = (\(\sqrt {2}\))² = 2

B = (\(\sqrt {3}\))² = 3

C = \(\sqrt {6}\)

⇒ A² +B² +C² = 4 + 9 + 6 = 19