+1237 Find all ordered pairs x, y of real numbers such that x+y=10 and x^3+y^3=300.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).
+129630 x + y = 10 square both sides
x^2 + y^2 + 2xy = 100
x^2 + y^2 = 100 - 2xy
x^3 + y^3 = 300
(x + y) ( x^2 + y^2 - xy) = 300
(10) ( 100 - 3xy) = 300
100 - 3xy = 30
100 - 30 =3xy
70 / 3 = xy
y = 70 / (3x)
x + y =10
x + 70 / (3x) = 10 multiply through by x
x^2 + (70/3) = 10x
x^2 -10x + 70/3 = 0
3x^2 - 30x + 70 = 0
x = [30 +/- sqrt [ 900 - 840 ] ] / 6 = [ 30 +/- sqrt 60 ] / 6 = 5 + sqrt (15) / 3 or 5 - sqrt (15) / 3
(x,y) = ( 5 + sqrt (15) / 3 , 5 -sqrt (15) / 3 ) or (5 - sqrt (15) / 3 , 5 + sqrt (15) / 3 )
