Question

A two-digit number is made of two consecutive digits such that the sum of
their squares is 4 less than the number. Find the two-digit number.

Answer 1

Answer:

Let the number be 10a+b where |a−b|=1 . Now a2+b2=10a+b−4.

Case 1: a>b.

Then a2+(a−1)2=10a+a−1–4 or 2a2–13a+6=0. So a=6 and the number is 65.

Case 2: a<b

Then a2+(a+1)2=10a+a+1–4 or 2a2–9a+4=0. So a=4 and the number is 45.