Question

If 2/3x+3/2y=5 and xy=6 find the value of 4/9x^2+9/4y^2​

Answer 1

$\huge \mid \red{ \textbf{Given}} \mid \\ \frac{2}{3x} + \frac{3}{2y} = 5 \: \: and \: \: xy=5 \\ \\ \huge \mid \red{ \textsf{Solution}} \mid \\ \frac{2}{3x} + \frac{3}{2y} = 5 \: \: \: \: \: \: {\sf{[squaring \: both \: sides \: ]}} \\ { (\frac{2}{3x} + \frac{3}{2y}) }^{2} = {5}^{2} \\ \\ \frac{4}{ {9x}^{2} } + \frac{9}{ {4y}^{2} } + \frac{2}{xy} = 25 \\ \\ \frac{4}{ {9x}^{2} } + \frac{9}{ {4y}^{2} } + \frac{2}{6} = 25 \\ \\ \frac{4}{ {9x}^{2} } + \frac{9}{ {4y}^{2} } = 25 - \frac{2}{6} \\ \\ \frac{4}{ {9x}^{2} } + \frac{9}{ {4y}^{2} } = \frac{148}{6} \\ \\ \frac{4}{ {9x}^{2} } + \frac{9}{ {4y}^{2} } = \frac{74}{3}$