Math Olympiad Problem | Nice Algebra Challenge

Math Olympiad Problem | Nice Algebra Challenge

[nishanth]

I briefly solved it in my mind like this!

if x² - xy = 14
x(x-y) = 14
That is, 7 × 2 = 14
7(7-5) = 14
So, x be 7 and y be 5

But this is only one solution!😅

[augustmathebula]

Can't you add the two equations and after that it becomes an equation of a circle centred at the origin. Then the x and y are coordinates of the center.

[vineetkaddu]

Great Problem. Did this Problem actually appear in any Olympiad? If so could you tell me which one? Great video as always

[elizabethjohns]

14/sqroot2 is not equal to 7*sqroot2

As well sqroot2 - 7*sqroot2 is not equal to -6