IMO 1959 - Problem 2

#olympiad #math #algebra #jee #trigonometry #geometry #gmat #mathstrick #olympiad2022
⭐ Join this channel / sqrtime
Follow me → / mathisstillfun
Subscribe → / sqrtime sub_confirmation=1
Instagram→ / mathisstillfun
Twitter for Physics: / gravityphy
PLAYLISTS 🎵 :
Algebra: • Algebra
Geometry: • Geometry
Indian Math Competitions: • Indian Competitions
Trigonometry: • Trigonometry

[@snjyjn]

At 4:45, when you replace the square root with the mod, I took a different path.
Since there are 2 possible square roots (one positive, and one negative), this becomes 2 equations (only the LHS shown):
2x+2(x-1), and
2x-2(x-1)
That still gives us the same 2 results, but without the same constraints on x.
A^2 = 2, or
x=(A^2 + 2)/4
If we try out A=1, and x=3/4 - with the right choice of +ve square root, or -ve square roots, the solution holds good.

[@SQRTime]

Interesting approach. Thanks for sharing

[@user-gh9ik2vu1w]

back in 1960 i could be a imo participant lol, today it is much tougher

[@evionlast]

Nice it's a simple problem liked it

[@SQRTime]

Nice 👍

[@ProbusMihraban]

Cool

[@SQRTime]

Thanks for checking 👍