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प्रश्न
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a" + (1)/"a"`
उत्तर
`"a" - (1)/"a"` = 3
Squaring both sides, we get
`("a" - 1/"a")^2`
= `"a"^2 + (1)/"a"^2 - 2`
= 9
⇒ `"a"^2 + (1)/"a"^2`
= 11.
Now,
`("a" + 1/"a")^2`
= `"a"^2 + (1)/"a"^2`
= 11 + 2
= 13
⇒ `"a" + (1)/"a"^2`
= ±`sqrt(13)`.
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