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Question
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
Solution
We have,
`(3x + 5y)^2 = (3x)^2 + (5y)^2 + 2 xx 3x xx 5y`
`=> (3x + 5y)^2 = 9x^2 + 25y^2 + 30xy`
`= 181 + 30(-6)` [∵ `9x^2 + 25y^2 = 181` and xy = -6]
= 181 - 180
`=> (3x + 5y)^2 = 1`
`=> (3x + 5y)^2 = (-+1)^2`
`=> 3x + 5y = +-1`
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