Can you Pass Stanford University Admission Exam ? | Find (x,y)=?

[@kareolaussen819]

Define a=3^x, b=-3^y. We have (a+b)=3, ab=-3, so a,b must be the roots of t^2-3t-3 =0, or (t-3/2)^2 = (9+12)/4. From this 3^x = a = (√21 + 3)/2, 3^y=-b=(√21-3)/2.