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