1992 IMO Problem #2

Topic: Algebra
Subtopic: Functional Equations

[imaginary]

I'm here just wondering, how on earth do people come up with all these weird substitutions or with the proofs with a square root of t-s

[owenvermeulen]

Cant you just let y=0, then f(x^2+f(0))=(f(x))^2. subsitute (f(x))^2 into original equation to get f(x^2+f(y))=y+f(x^2+f(0)) and see that it increases as y increases? Or am I completely wrong, definitely possible haha

[yashvardhan]

Why did u not use bijectivity which directly concludes from x=0, It would be much faster.

[mineralstones]

can you solve this problem: find F :R-R such that setisfy this equation x, y not equl zero, F((1/x)+(1/y)) +F(x+y)=1

[parvinmuzaffarov]

how can you apply f to both side w/out proving the “ if a=b then f(a)=f(b) ?”