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

Solution (By Examveda Team)

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
$$\eqalign{ & = \frac{3}{4} \times \left( { - \frac{4}{3}} \right) + 2 \times 3 \cr & = - 1 + 6 \cr & = 5 \cr} $$