If 22x – y = 16 and 2x + y = 32, the value of xy is

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If 2^{2x – y} = 16 and 2^{x + y} = 32, the value of xy is

1. 2
2. 4
3. 6
4. 8

Correct Option: C

2^{2x – y} = 16 = 2⁴
⇒ 2x – y = 4 ............... (i)
2^{x + y} = 32 = 2⁵
⇒ x + y = 5 ............... (ii)
On adding equations (i) and (ii),
3x = 9 ⇒ x = 3
From equation (ii),
y = 5 – x = 5 – 3 = 2
∴ xy = 3 × 2 = 6