Question

if 3x-2y=7 and xy=3, then find the value of (3x+2y)²

Answer 1

Answer:

$3x - 2y = 7 .........(1)\\ xy = 3 \: ..........(2) \\ from \: equation \: 2 \\ x = \frac{3}{y} \\ put \: the \: value \: of \: x \: in \: equation \: (1) \\ 3( \frac{3}{y}) - 2y = 7 \\ \frac{9}{y} - 2y = 7 \\ \frac{9 - 2 {y}^{2} }{y} = 7 \\ 9 - 2 {y}^{2} = 7y \\ - 2 {y}^{2} - 7y + 9 = 0 \\ - (2 {y}^{2} + 7y - 9) = 0 \\ 2 {y}^{2} + 7y - 9 = 0 \\ 2 {y}^{2} + 9y - 2y - 9 = 0 \\ y(2y + 9) - 1(2y + 9) = 0 \\ (y - 1)(2y + 9) = 0 \\ y = 1 \\ y = \frac{ - 9}{2} \\ two \: values \: of \: y \:$

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