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Question
If `"a" + 1/"a" = 6;`find `"a" - 1/"a"`
Solution
`("a" + 1/"a")^2`
= `("a"^2) + 2("a") (1/"a") + (1/"a")^2`
= `"a"^2 + (1)/"a"^2 + 2`
⇒ 36 = `"a"^2 + (1)/"a"^2 + 2`
⇒ `"a"^2 + (1)/"a"^2`
= 34
`("a" - 1/"a")^2`
= `("a")^2 - 2("a") (1/"a") + (1/"a")^2`
= `"a"^2 + 1/"a"^2 - 2`
= 34 - 2
= 32
⇒ `"a" - 1/"a"`
= ±`sqrt(32)`
= ± 4`sqrt(2)`.
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