Problem 9 · 2022 Math Kangaroo
Medium
Algebra & Patterns
substitution
How many real solutions does the equation \((x-2)^2 + (x+2)^2 = 0\) have?
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Answer: A — 0
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Hint 1 of 2
A sum of two squares equals zero only when both squares are zero.
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Hint 2 of 2
Can x = 2 and x = −2 hold at the same time?
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Approach: sum of squares = 0
- (x−2)^2 + (x+2)^2 = 0 needs both terms to vanish at once.
- That forces x = 2 and x = −2 simultaneously, which is impossible.
- So there are 0 real solutions.
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