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)
Answer & explanation
Correct answer: option 3
⇒ 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