Because 0 < y < 1

So y = 0.xxxx.

Because the root number is 3 =1.732xxx.

So Y= root number 3- 1. (The rest are decimal parts)

Because x is an integer (no fractional part). Root number 3 = 1.732xxx. 10+ root number 3 = x+y.

So x =10+1=11.

So X-Y= 1 1- (radical number 3-1) =1-radical number 3+ 1= 12- radical number 3.

The reciprocal of 12- radical 3 is -( 12- radical 3)=- 12+ radical 3.