A Nice System of Equations | Math Olympiad | Algebra

[@mohammedsaysrashid3587]

Amazing introduction...thanks Sir🙏 for sharing .....(x:y)(3,3)

[@SidneiMV]

simply amazing!

[@Quest3669]

(X; Y)= (3;3) {( 9+ -√57)/ 2 ;( 9 - + √ 57)/2}

[@潘博宇-k4l]

(X, Y)=(3, 3), ([9+(57)^(1/2)]/2, [9-(57)^(1/2)]/2), ([9-(57)^(1/2)]/2, [9+(57)^(1/2)]/2).

[@RashmiRay-c1y]

x+y=a and xy=b. Then, a+b=15 and ab =54 > (a,b) = (9,6), (6,9). If a=6, b=9 > x=y=3. If a=9, b=6, x=1/2[9 +/-√57], y = 1/2[9-/+√57].

[@batavuskoga]

How did you get : a²-15a+54=0 ? Explanation step by step, please. You have the same some time later with x²-6x+9=0 and x²-9x+6=0. I understand the other parts of the video

[@Bertin-q3y]

X=3. Y=3 X=(9-57^0,5)/2. Y=( 9+57^0,5)/2 et reciproquement

[@hjs6102]

Well I see the thumb and say 3 within one second.

[@Shobhamaths]

Let a=x+y, b=xy;a^2-15a+54=0, (a, b) =(6,9) ;(9, 6), (x, y) =(3, 3), (9±√57) /2 , ((9-√57) /2, (9+√57) /2)👍

[@RealQinnMalloryu4]

xy(x+y)=54 (2)(14+13)=54 2^27 2^3^3 2^3^13^1 2^3^1^1^1 2^3 (xy ➖ 3xy+2) .(x+1)+(y+1)=16 ((7)+1)+((7)+1)=16 8^8 2^3^2^3 1^1^2^1 2^1 (xy ➖ 2xy+1) .