Question

A number consist of two digits the digit in tens place is greater than the unit place by 4 sum of square of digit of number is 15 less than the number find the 2 numbers

Answer 1

Let the number be 10 x + y
The tens digit exceeds its unit digit by 4
⇒ x - y = 4 ⇒ x = 4+y
Sum of square of its digits is 15 less than the number
⇒ x² + y² = 10 x + y - 15 
(4+y)² + y² = 10 (4+y) + y - 15
16+y²+8 y +y² = 40 + 10 y + y - 15
16 + 2 y² +8 y = 25 + 11 y
16 + 2 y² + 8 y -25 - 11 y =0
2 y² - 3 y - 9 =0
2 y² - 6 y + 3 y - 9 = 0
2 y (y -3) + 3(y-3) = 0
(y-3) (2 y + 3) = 0
 y = 3 or - 3/2
Rejecting y = -3/2 therefore y = 3 
x = 4 +3 = 7
Therefore the number is 73.