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If $(x + y)^2 = 45$ and $xy = 10$, what is $(x - y)^2$?

 Apr 9, 2018
 #1
avatar+100456 
+2

(x + y)^2  =  45    ⇒  x^2 + 2xy + y^2   =  45     (1)

 

xy  = 10    (2)

 

Sub (2)  into (1)

 

x^2 + 2(10) + y^2  = 45

x^2 + y^2  + 20  = 45       subtract 20 from both sides

x^2 + y^2  =  25 

 

Finally....

(x  - y)^2  = x^2 - 2xy + y^2  = 

(x^2 + y^2) - 2xy  =  

(25)- 2(10)

25 - 20  =

5

 

 

cool cool cool

 Apr 9, 2018
 #2
avatar+1354 
+13

Awesome job CPhill

 Apr 9, 2018
 #3
avatar+1354 
+13

smileycool Hey

 Apr 9, 2018

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