Question

Answer of Q . if x-y=13 & root x+ root y =13

Answer 1

Let √x = a and √y = b ,




Given, √x + √y = 13

= > a + b = 13 -----: ( 1 )




According to the question :



= > x - y = 13


$= > ( \sqrt{x} ) {}^{2} - {( \sqrt{y}) }^{2} = 13$


= > a² - b² = 13


= > ( a + b ) ( a - b ) = 13



Putting values from ( 1 ) ,



= > 13 ( a - b ) = 13


= > a - b = 13 / 13


= > a - b = 1


= > a = b + 1



Putting values in ( 1 ),



= > a + b = 13


= > b + 1 + b = 13


= > b = 6



So,
a + b = 13
a = 13 - 6
a = 7




Therefore,

√x = 7

So, x = 7²

x = 49



And,



√y = 6

So, y = 6²

y = 36

$\boxed{ \bold{ \underline{x = 49 \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \: \: y = 36}}}$