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Question
If a + b = 7 and ab = 10; find a - b.
Solution
a + b = 7 and ab = 10
⇒ a (7 − a) = 10
⇒ 7a − a2 = 10
⇒ a2 − 7a + 10 = 0
⇒ a2 − 5a − 2a + 10 = 0
⇒ a (a − 5) − 2(a − 5) = 0
⇒ (a − 2) (a − 5) = 0
⇒ a = 5, 2
⇒ b = 2, 5
When a = 5, b = 2
⇒ a − b = 3
When a = 2,b = 5
⇒ a − b = −3
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