Question

The sum of the digits of a three-digit number is and the sum of the squares of its digits is . If we subtract from that number, we shall get a number consisting of the same digits written in the reverse order. Find the number.

Hard

Solution

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Let three digit number is

According to  question,

CONDITION 1: a sum of the digits of a three-digit number is 17

  i.e     

CONDITION 2: the sum of the squares of its digits is 109

i.e     

CONDITION 3: if we subtract 495 from that number, we shall get a number consisting of the same digits written in the reverse order

 i.e     






From

  

  

From




  which is a quadratic equation

on solving we get


is not possible as digit of any number can't  be a fraction
hence,


now,
from

thus,
the required number is 


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