China | A Nice Algebra Problem | Math Olympiad

[@aravindhnagarathinam]

Exciting

[@SALogics]

Thank you so much! ❤

[@LITHICKROSHANMS-gw2lx]

Very nice sir!

[@SALogics]

Thanks for liking. ❤

[@SGuerra]

Bela questão! Parabéns pela escolha!

[@SALogics]

muito obrigado!

[@walterwen2975]

Math Olympiad: (√2)^√x - (√2)^√y = 28; x, y =?
(√2)^√x > 28 > (√2)^√y, x > y > 2, 28 = 4(7) = 4(8 - 1) = 32 - 4 = 2^5 - 2^2
(√2)^√x - (√2)^√y = 28 = 2^5 - 2^2 = (√2)^10 - (√2)^4 = (√2)^√100 - (√2)^√16
x = 100, y = 16
Answer check:
x = 100, y = 16: (√2)^√x - (√2)^√y = 28; Confirmed as shown
Final answer:
x = 100, y = 16

[@SALogics]

Very nice! I really appreciate that ❤

[@patk5724]

There is also another result such as:
x = 144 and
y = 16(log6/log2)^2
You can proof check it to confirm result etc...

[@SALogics]

Very nice! ❤

[@haticekoca5716]

2^x-2^y=28 28=7,4
2^4-2^7
2^4= 16
2^7=128-28= 100
x=100 y=16

[@SALogics]

Very nice trick! ❤

[@sandytanner9333]

X=100 y=16

[@SALogics]

Yes, you are right! ❤

[@user-qr7dw4hk6x]

32-4, вот и всё. Думал три секунды

[@SALogics]

Очень хорошо! ❤