Problem 9 · 2010 Math Kangaroo
Medium
Algebra & Patterns
sum-constraint
How many two-digit numbers with x in the tens column and y in the units column have the property (x−3)² + (y−2)² = 0?
Show answer
Answer: A — 1
Show hints
Hint 1 of 2
A sum of two squares equals zero only one way.
Still stuck? Show hint 2 →
Hint 2 of 2
Each square must be zero on its own.
Show solution
Approach: sum of squares is zero only when each term is zero
- (x−3)² + (y−2)² = 0 forces both squares to be 0.
- So x = 3 and y = 2, giving the single number 32.
- Exactly 1 two-digit number works.
Mark:
· log in to save