Find real numbers x and y such that x + y = 6 and xy = 7

[jwpaine]

"Find real numbers x and y such that x + y = 6 and xy = 7"

I setup a system of equations:

{x + y = 6
{xy = 7

solve for y by substitution:

x = (y - 6)
(y - 6)y = 7
-y^2 + 6y -7 = 0

I complete the square to get my too zeros: y = 3 + sqrt(2) and y = 3 - sqrt(2)

do I now plug in those two irrational values of y and solve for the two solutions of x?


Thanks, it's been a little while since I did this.

 

[tkhunny]

You need Real. Irrational is okay.

Yes, use one y-value to find the related x-value.