Problem 13 · 2018 Math Kangaroo
Hard
Algebra & Patterns
\(\lvert\sqrt{17} - 5\rvert + \lvert\sqrt{17} + 5\rvert = {}\)?
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Answer: A — \(10\)
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Hint 1 of 2
Compare √17 with 5 to drop the absolute-value signs.
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Hint 2 of 2
One term is positive inside, the other negative.
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Approach: resolve each absolute value by sign, then add
- Since √17 ≈ 4.12 < 5, we have |√17−5| = 5−√17.
- And |√17+5| = √17+5.
- Their sum is (5−√17)+(√17+5) = 10.
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