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Question
If x + y = 9, xy = 20
find: x - y
Solution
x + y = 9, xy = 20
We know (a + b)
= a2 + 2ab + b2
∴ (x + y)2
= 81 x2 + y2 + 2xy
⇒ x2 + y2
= 81 - 2(120)
= 41
We also know (a - b)2
= a2 - 2ab + b2
⇒ (x - y)2
= x2 - 2xy + y2
⇒ (x - y)2
= 41 - 2(20)
= 1
⇒ x - y
= ±1.
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