Math Olympiad Problem | A Nice Algebra Problem | Find the Value of x and y

[@Mathsgurulk]

Thanks sir

[@RyanLewis-Johnson-wq6xs]

(X^2+Y^2+XY)/(2XY)=7/4 (X^3+Y^3)/(2XY)=9/4 X=2 Y=1 final answer

[@andryvokubadra2644]

(x² + y² + xy)/(2xy) = 7/4 (x² + y² + xy)/xy = 7/2 --> xy = 2 --> x² + y² = 5 (x³ + y³)/(2xy) = 9/4 (x³ + y³)/xy = 9/2 --> xy = 2 --> x³ + y³ = 9 xy = 2 --> x,y = -2,-1 x,y = -1,-2 x,y = 1,2 x,y = 2,1 Let x,y = -2,-1 x² + y² = 5 (-2)² + (-1)² = 5 4 + 1 = 5 --> match Becouse x² + y² = 5 is a quadratic equation so all (x,y) values are match. Not sure? Proof it !!! Becouse x³ + y³ = 9 is cubic equation so just (x,y) positif numbers is possible correct. Not sure? Proof it !!! Let x,y = 1,2 x³ + y³ = 9 1³ + 2³ = 9 1 + 8 = 9 --> match Let x,y = 2,1 x³ + y³ = 9 2³ + 1³ = 9 8 + 1 = 9 --> match So the root values (x,y) = 1,2 and 2,1

[@cristiandumitru7588]

(x, y)=(1, 2); (2, 1)