If x+y=-6andxy=9sox^2+y^2

Question

If x+y=-6 and xy=9 then x^2+y^2=?

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Thank you.

 

Answer 1

(x+y)(x+y) = x² + 2xy + y²

 

Substituting the given values, we have (-6)(-6) = x² + y² + 2(9)

 

                                                               36 = x² + y² + 18

 

                                                       x² + y² = 18

 

Answer 2

Here's a little more detail.  I had to work through it to see how Mark got there!

x+y = -6

y = -6-x

Substitute this into the second equation.

xy = 9

x(-6-x) = 9

-6x-x² = 9

rearrange it:

-x²-6x-9 = 0

mutliply both sides by -1

x²+6x+9 = 0

(x+3)(x+3) = 0

x = -3

 

x+y = -6

-3 + y = -6

y = -3

 

x² + y² = 9+9 = 18