Question

Number s is equal to the square of the sum of the digits of a 2 digit number
d. if the difference between s and d is 27, then d is

Answer 1

Heya user, 

Let two digit no. be d = [ 10x + y ] ...

Then x² + y² = s
Now, d - s = 10x + y - x² - y²
=> 27 = 10x + y - x² - y²
=> ( x² - 10x + 100 ) +  ( y² - y + 1/4 ) = 73 + 1/4
=> ( x - 10 )² + ( y - 1/2 )² = 73 + 0.25

By hit and trial, we see, only y = 9, x = 1 satisfies the eqn.
Since, 1² + 8.5² = 1 + 72.25 = 73.25

.'. the no. is 19 ....