Question

please solve the above question.​

Answer 1

Answer:

$x - y = - 2.$

Step-by-step explanation:

$x = \sqrt{63 + 2 \sqrt{63 + 2 \sqrt{63 + ....} } } \\ \\ then \: \: \: \: x = \sqrt{63 + 2x } \\ \\ {x }^{2} - 2x - 63 = 0 \\ \\ {x}^{2} - 9x + 7x - 63 = 0 \\ \\ x(x - 9) + 7(x - 9) = 0 \\ \\ (x + 9)(x - 7) = 0 \\ \\ x = 7 \\ \\ \\ \\ \\ \\ \\ \\ y = \sqrt{63 - 2y} \\ \\ {y}^{2} + 2y - 63 = 0 \\ \\ {y}^{2} - 7y + 9y - 63 = 0 \\ \\ y(y - 7) + 9(y - 7) = 0 \\ \\ (y - 9)(y + 7) = 0 \\ \\ y = 9 \\ \\ \\ x - y = 7 - 9 = - 2.$