Japanese Math Olympiad Question | You should know this trick!

This is an interesting question with amazing concepts!
Hope you are well
Playlist to watch all videos on Learncommunolizer
• Maths Olympiad
And
• Maths
Subscribe: / @learncommunolizer

[@Zarunias]

With these small numbers I actually was way faster by just doing the calculations with the actual numbers.

[@rdeviltron]

I love your videos so much and I've subscribed since you had 70.000 subscribers. Keep the great work going to get your 100k subs.

[@MrHaiopei]

Vielen Dank, hat Spaß gemacht

[@learncommunolizer]

Thank you very much

[@walterwen2975]

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

[@user-rq9po2zv4k]

Вумничка 😊❤

[@lthakur92411]

I think this is very long method,

[@Billts]

Τι μας έδειξε η πράξη αυτή;