Suppose xy=9 and (x+y)2 = 21. What is x2+y2?

Question

Suppose xy=9 and (x+y)² = 21. What is x²+y²?

 

a) 3

b) 12

c) 36

d) 81

Answer 1

Use F-O-I-L (First-Outside-Inside-Last) to expand:

      (x+y)² = (x+y)(x+y) = x² + xy + yx + y² = x² + 2xy + y² = 21

                                                                      x² + 2(9) + y² = 21

                                                                      x² + y² = 3

 

Answer 2

One of the given facts can be expanded (squaring the binomial): x²+2xy+ y² = 21²

 

So x² + y² = 441 - 2(xy) but we know that xy = 9, so

x² + y² =441 - 2(9) = 423.

 

SUBSEQUENT EDITING:  The 21 should not be squared...so we should get

x² + y² = 21 - 2(9) = 3.