Question

Find the value of 9x^2+25y^2, if (3x-5y)=19 and xy =5​

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Answer 1

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Answer 2

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$9 {x}^{2} + 25 {y}^{2} \\ squaring \: both \: sides \\ {(3x - 5y)}^{2} = {19}^{2} \\ 9 {x}^{2} + 25 {y}^{2} - 30xy = 361 \: \: \: (xy = 5) \\ 9 {x}^{2} + 25 {y}^{2} - 150 - 361 \\ 9 {x}^{2} + 25y^{2} - 511 \\ = 511$