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Question
If `"a" - 1/"a" = 10;` find `"a" + 1/"a"`
Solution
`"a" - 1/"a" = 10`
`("a" - 1/"a")^2`
= `"a"^2 + 1/"a"^2 - 2("a") (1/"a")`
⇒ (10)2
= `"a"^2 + 1/"a"^2 - 2`
⇒ `"a"^2 + 1/"a"^2`
= 102
Now, `("a" + 1/"a"^2)`
= `"a"^2 + 1/"a"^2 + 2("a") (1/"a")`
= 102 + 2
= 104
⇒ `"a"^2 - 1/"a"^2`
= `sqrt(104)`
= ±2`sqrt(26)`.
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