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Question
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a" + (1)/"a"`
Solution
Using (a + b)2 = a2 + 2ab + b2
`("a" + 1/"a")^2`
= `"a"^2 + 2"a"(1/"a") + (1/"a")^2`
⇒ `("a" + 1/"a")^2 = "a"^2 + 2 + (1)/"a"^2`
⇒ `("a" + 1/"a")^2 = "a"^2 + (1)/"a"^2 + 2`
⇒ `("a" + 1/"a")^2` = 14 + 2
⇒ `("a" + 1/"a")^2` = 16
⇒ `"a" + (1)/"a"` = ±4.
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