How can we show that there are no (x,y) pairs of real numbers that satisfy xy = 3 and (x + y)^2 = 10 ? Intuitively it's obvious but I'm not sure exactly how to show it..
How can we show that there are no (x,y) pairs of real numbers that satisfy xy = 3 and (x + y)^2 = 10 ? Intuitively it's obvious but I'm not sure exactly how to show it..
Brute force:
Sub y = 3/x into (x + y)^2 = 10.
After expanding and simplifying you get . Multiply through by x^2 and re-arrange: