> Hi! > > Here are two questions that have me really stumped. > > Q1 - If x + y = 2 and x^2 + y^2 = 8, find > > a) xy > b) x - y > > Do I solve these simultaneously? Quadratically? Or > something else? Use the fact that (x+y)^2= x^2+ 2xy+ y^2. Since x+y= 2, (x+y)^2= 4. Since x^2+ y^2= 8, that equation becomes 4= 8+ 2xy.
For x-y, use the fact that (x-y)^2= x^2- 2xy+ y^2. You know that x^2+ y^2= 8 and you just found 2xy so you can find (x-y)^2 and then x- y.
> > Q2 - Complete the sequence: > > 7/8, 2/3, 1/2, 4/11, 1/4, ______, ______ . > > I seriously can't figure out any pattern here! > > Thanks.