Question

Find the values of x and y:
5+3√2/5-3√2=X+y√2

PL ANSWER FAST. THIS QUESTION IS FROM CLASS 9.​

Answer 1

$\frac{5 + 3 \sqrt{2} }{5 - 3\sqrt{2} } = x + y \sqrt{2} \\ \frac{5 + 3 \sqrt{2} }{5 - 3 \sqrt{2} } \times \frac{5 + 3 \sqrt{2} }{5 + 3 \sqrt{2} } = x + y \sqrt{2} \\ \frac{( {5 + 3 \sqrt{2} })^{2} }{ {5}^{2} - ( {3 \sqrt{2} })^{2} } = x + y \sqrt{2} \\ \frac{25 + 18 + 30 \sqrt{2} }{25 - 18} = x + y \sqrt{2} \\ \frac{43 + 30 \sqrt{2} }{7} = x + y \sqrt{2} \\ \frac{43}{7} + \frac{30}{7} \sqrt{2} = x + y \sqrt{2} \\ comparing \: both \: sides \\ x = \frac{43}{7} \: \: \: \: \: \: \: \: \: \: y = \frac{30}{7}$