If (x + y)^2 = 100, (x - y)^2 = 16, find value of xy

[Sarah2391]

If (x+y)squared = 100 and (x-y)squared = 16, what is the value of xy?

(a) 14

(b) 21

(c) 121

(d) 1600

(e) 64

How to solve?

 

[pka]

Re: Help!!

\(\displaystyle \begin{array}{l} x^2 + 2xy + y^2 = 100 \\ x^2 - 2xy + y^2 = 16 \\ \end{array}\)
Substract the second from the first.

 

[Sarah2391]

Re: Help!!

Thank you! Now I remember the formula

 

[Sarah2391]

Re: Help!!

Just to check, what did you get as the value of xy?

 

[Denis]

What did YOU get ?!

 

[Loren]

Taking the square root of both sides of both given equations yields...
x+y=+/-10
x-y=+/-4

This leads to (7,3), (-7,-3), (3,7), or (-3,-7).
Therefore xy=what?