How many two digit positive integers N have the property that the sum of N and number obtained reversing the order of the digits of N is a perfest square?

Asked by Shivendra | 23rd Jul, 2017, 01:49: PM

Expert Answer:

begin mathsize 16px style Let space straight N equals 10 straight x plus straight y
Then comma space we space should space have
left parenthesis 10 straight x plus straight y right parenthesis plus left parenthesis 10 straight y plus straight x right parenthesis equals Perfect space square
rightwards double arrow 11 straight x plus 11 straight y equals Perfect space square
rightwards double arrow 11 left parenthesis straight x plus straight y right parenthesis equals Perfect space square
This space is space possible space only space when space straight x plus straight y equals 11
Then comma space we space have
straight x plus straight y equals 2 plus 9 equals 11
straight x plus straight y equals 3 plus 8 equals 11
straight x plus straight y equals 4 plus 7 equals 11
straight x plus straight y equals 5 plus 6 equals 11
straight x plus straight y equals 6 plus 5 equals 11
straight x plus straight y equals 7 plus 4 equals 11
straight x plus straight y equals 8 plus 3 equals 11
straight x plus straight y equals 9 plus 2 equals 11
Such space 8 space solutions space are space possible. end style

Answered by Rashmi Khot | 24th Jul, 2017, 09:45: AM