Question

If (3x - 5y) = 10 and xy=5, then find the value of 9x2 +25y2.​

Answer 1

Answer:

$\huge\boxed{\tt\implies: 249}$

Step-by-step explanation:

$\bf(3x - 5y) = 10 - - - - - - - (1) \\\bf \: \: xy=5 \bf\implies: x = \frac{5}{y} \\ \\ \bf \: value \: of \: x \: put \: in \: (1) \\ \tt\implies: 3 \times \frac{5}{y} - 5y = 10 \\ \\\tt\implies: \frac{15 - {5y}^{2} }{y} = 0 \\ \\ \tt\implies: 15 - {5y}^{2} = 0 \\ \\ \tt\implies: {5y}^{2} = 15 \\ \\ \tt\implies: {y}^{2} = \frac{15}{5} \\ \\ \tt\implies: {y}^{2} = 3 \\ \\ \boxed{\tt\implies: y = \pm\sqrt{3} } \\ \\ \tt\implies: value \: of \: x = \frac{5}{ \sqrt{3} } or \: - \frac{5}{ \sqrt{3} } \\ \\ \sf \therefore \: {9x}^{2} + {25y}^{2} \\ \\ \tt\implies: 9 \times( { \frac{5}{ \sqrt{3} } })^{2} + 25 \times { \sqrt{3} }^{2} \\ \\ \tt\implies: \frac{9 \times 25}{3} + 25 \times 3 \\ \\ \tt\implies: \frac{225 + 522}{3} \\ \\ \tt\implies: \frac{747}{3} \\ \\ \boxed{\tt\implies: 249}$