If 16x2 + 9y2 + 4z2 = 24(x - y + z) - 61, then the value of (xy + 2z) is:

Answer: Option D

16x² + 9y² + 4z² = 24(x - y + z) - 61
⇒ 16x² + 9y² + 4z² = 2 × 4x × 3 - 2 × 3x × 4 + 2 × 2z × 6
⇒ (4x - 3)² + (3y + 4)² + (2z - 6)² = 0
x = $$\frac{3}{4}$$
y = $$-\frac{4}{3}$$
z = 3
⇒ xy + 2z
$$\begin{array}{rl}& =\frac{3}{4}\times \left(-\frac{4}{3}\right)+2\times 3\\ & =-1+6\\ & =5\end{array}$$