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If 16x2 + 9y2 + 4z2 = 24(x - y + z) - 61, then the value of (xy + 2z) is:
Answer & Solution
Correct 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
$$\eqalign{ & = \frac{3}{4} \times \left( { - \frac{4}{3}} \right) + 2 \times 3 \cr & = - 1 + 6 \cr & = 5 \cr} $$
⇒ 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
$$\eqalign{ & = \frac{3}{4} \times \left( { - \frac{4}{3}} \right) + 2 \times 3 \cr & = - 1 + 6 \cr & = 5 \cr} $$
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