x + y = 6x+y=6"...................Eq1"...................Eq1
x^2 + y^2 = 20x2+y2=20"..............Eq2"..............Eq2
"Using the identity":Using the identity:color(red)(x^2+y^2=(x+y)^2-2xyx2+y2=(x+y)2−2xy
x^2+y^2=(x+y)^2-2xyx2+y2=(x+y)2−2xy
Substituting : x + y = 6 and x^2 + y^2 = 20x+y=6andx2+y2=20
20=(6)^2-2xy20=(6)2−2xy
36-2xy=2036−2xy=20
-2xy=-16−2xy=−16
xy=8xy=8
color(blue)(x=8/yx=8y
Substituting x=8/yx=8y in "Eq1"Eq1
8/y + y = 68y+y=6
8+y^2=6y8+y2=6y
y^2-6y+8=0y2−6y+8=0
(y-2)(y-4)=0(y−2)(y−4)=0
So, color(darkred)(y=2 or y=4y=2ory=4
When color(magenta)(y =2y=2
x+2=6x+2=6
color(magenta)(x=4x=4
When color(darkorange)(y =4y=4
x+4=6x+4=6
color(darkorange)(x=2x=2
~Hope this helps! :)