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Question
If 3x + 4y = 13 and xy = 1, find 3x − 4y.
Sum
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Solution
Here, 3x + 4y = 13, xy = 1,
Thus,
132 − (3x − 4y)2 = 4 × 3 × 4(1) ...[Using (3x + 4y)2 − (3x − 4y)2 = 4 × 3 × 4(xy)]
169 − (3x − 4y)2 = 48
∴ (3x − 4y)2 = 169 − 48
∴ (3x − 4y)2 = 121
∴ 3x − 4y = `+-sqrt121`
∴ 3x − 4y = ± 11
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