Mathematics
If 3x - 4y = 16 and xy = 4, find the value of 9x2 + 16y2.
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Answer
We know that,
a2 + b2 = (a - b)2 + 2ab.
9x2 + 16y2 = (3x)2 + (4y)2 = (3x - 4y)2 + 24xy.
Substituting values we get,
⇒ 9x2 + 16y2 = (16)2 + 24 × 4
⇒ 9x2 + 16y2 = 256 + 96
⇒ 9x2 + 16y2 = 352.
Hence, 9x2 + 16y2 = 352.
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