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Question
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
Solution
`(2x + 3y)^2 = (2x)^2 + (3y)^2 + 2(2x)(3y)`
`=> (2x + 3y)^2 = 4x^2 - 9y^2 + 12xy`
`=> (8)^2 = (4x^2 + 9y^2 + 24)` [∵ 2x + 3y = 8, xy = 24]
`=> 64 - 24 = 4x^2 + 9y^2`
`=> 4x^2 + 9y^2 = 40`
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