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Question
If 3x - 7y = 10 and xy = -1, find the value of `9x^2 + 49y^2`
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Solution
We have
`(3x - 7y)^2 = (3x)^2 + (-7y)^2 - 2(3x)(7y)`
`= 9x^2 + 49y^2 - 42xy`
`=> [10]^2 = 9x^2 + 49y^2 - 42xy` [∵ 3x - 7y = 10]
`=> 100 = 9x^2 + 49y^2 - 42[-1]` [∵ xy = -1]
`=> 100 - 42 = 9x^2 + 49y^2`
`=> 9x^2 + 49y^2 = 58`
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