Question

What adds to equal 6 but multiplies to make 4?

Answer 1

x+y=6
x*y=4 => y=4/x

x +4/x = 6

x^2 +4 = 6x

x^2 -6x +4=0

D = 36-16=20

x_1,2 = (6+/- sqrt20)/2

x_1,2 = (6+/- 2sqrt5)/2 = 2(3+/- sqrt5)/2 = 3+/- sqrt5

x_1,2 = 3+/- sqrt5

y_1 = 4/x_1 = 4/(3-sqrt5) = (4(3+sqrt5))/(9-5) = (4(3+sqrt5))/4 = 3+sqrt5

y_2 = 4/x_2 = 4/(3+sqrt5) = (4(3-sqrt5))/(9-5) = (4(3-sqrt5))/4 = 3-sqrt5

hope helped