Question

A positive two-digit number is represented by 10t + u. The sum of the squares of the digits is 26. If the number is decreased by the number with its digits reversed, the result is 36. Find the two-digit number.

Answer 1

"The sum of the squares of the digits is 26"
10t + u = 26  ---->(1)

"If the number is decreased by the number with its digits reversed, the result is 36"
u - 10t =36 -----> (2)

By subtracting the equation we can find t.
  u+10t = 26)
-(u-10t=36)
______________
0u  +20t = 26 -36
---> 20t = -10
t= -10/20
t= -1/2

Inserting value t in (1)
10t + u = 26 
10(-1/2) + u= 26
-5+u=26
u= 26+5 = 31

Using u and t in the original expression 10t+u express a positive number

10t+u
= 10(-1/2) +u
= -5 + 31
= 26
----> Proves this statement is true 
"The sum of the squares of the digits is 26"
10t + u = 26