Find all pairs (x, y) of real numbers such that x+y=10 and x^2+y^2=56
Thanks :)
x + y = 10 ---> x = 10 - y
x2 + y2 = 56 ---> (10 - y)2 + y2 = 56
(100 - 2y + y2) + y2 = 56
100 - 2y + 2y2 = 56
2y2 - 2y + 44 = 0
y2 - y + 22 = 0
Using the quadratic formula: y = 5 +/- sqrt(3)
x = 5 -/+ sqrt(3)
Answers: ( 5 + sqrt(3), 5 - sqrt(3) ) and ( 5 - sqrt(3), 5 + sqrt(3) )