Math Olympiad | A Beautiful Exponential Problem | VIJAY Maths

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[@walterwen2975]

Math Olympiad: √[(5⁸ + 7⁸ + 74⁴)/2] = ?
Let: a = 25, b = 49; 5⁸ + 7⁸ + 74⁴ = 25⁴ + 49⁴ + (25 + 49)⁴ = a⁴ + b⁴ + (a + b)⁴
a⁴ + b⁴ + (a + b)⁴ = a⁴ + b⁴ + (a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴)
= 2(a⁴ + 2a³b + 3a²b² + 2ab³ + b⁴) = 2[(a⁴ + 2a²b² + b⁴) + (2a³b + 2ab³) + a²b²]
= 2[(a² + b²)² + 2ab(a² + b²) + a²b²] = 2(a² + ab + b²)²
√[(5⁸ + 7⁸ + 74⁴)/2] = [√2(a² + ab + b²)²/2] = a² + ab + b² = 25² + (25)(49) + 49²
= 625 + 25(50 - 1) + (50 - 1)² = 625 + 1250 - 25 + 2500 - 100 + 1 = 4251

[@daakudaddy5453]

In the end you got
a^2 + b^2 + ab
You could have written it as
(a + b)^2 - ab
= 74^2 - (25 x 49)
This is much easier to calculate.

[@ManojkantSamal]

Respected Sir, Good afternoon. I prefer the way, you make reach the problem to the end....

[@vijaymaths5483]

So nice of you ,Thanks for watching!

[@lyricsssulders43]

👏👏👏

[@pratapjadhao388]

Thanks sir,
For the memory booster example.... . .

[@Danieswors]

4251

[@ManojkantSamal]

(25)^2+(25×49)+(49)^2
625+1225+2401=4251(may be)

[@crazyindianvines1472]

great explanation

[@prabhushettysangame6601]

One of the best example I liked 👍

[@ezzatabdo5027]

High concentration and high flexibility by best explanation, thanks too much sir.

[@naveenkhare1979]

Very nice but typical problem

[@vijaymaths5483]

Thank you ⚘️