Japanese Math Olympiad Question | You should know this trick!
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- เผยแพร่เมื่อ 4 ก.ค. 2024
- This is an interesting question with amazing concepts!
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With these small numbers I actually was way faster by just doing the calculations with the actual numbers.
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Japanese Math Olympiad Question: √[(100² + 81² + 19⁴)/2] = ?
100² + 81² + 19⁴ = 10⁴ + 9⁴ + 19⁴; Let: a = 10, b = 9
100² + 81² + 19⁴ = a⁴ + b⁴ + (a + b)⁴, a⁴ + b⁴ = (a² + b²)² - 2a²b²
(a + b)⁴ = [(a + b)²]² = (a² + b² + 2ab)² = (a² + b²)² + 4ab(a² + b²) + 4a²b²
a⁴ + b⁴ + (a + b)⁴ = 2(a² + b²)² + 4ab(a² + b²) + 2a²b²
= 2[(a² + b²)² + 2ab(a² + b²) + a²b²] = 2(a² + b² + ab)²
√[(100² + 81² + 19⁴)/2] = √{[2(a² + b² + ab)²]/2} = a² + b² + ab
= 10² + 9² +(10)(9) = 100 + 81 + 90 = 271
I think this is very long method,
Τι μας έδειξε η πράξη αυτή;