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Question
If a - b = 10 and ab = 11; find a + b.
Solution
a - b = 10, ab = 11
We know that :
(a - b)2 = a2 - 2ab + b2
⇒ (10)2 = a2 + b2 - 2 x 11
⇒ 100 = a2 + b2 - 22
⇒ a2 + b2
= 100 + 22
= 122
Using (a + b)2 = a2 + b2 + 2ab, we get
(a + b)2
= 122 +2(11)
= 122 + 22
= 144
⇒ (a + b)
= `sqrt(144)`
= ±12.
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