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Question
If `("a" + 1/"a")^2 = 3`; then show that `"a"^3 + (1)/"a"^3 = 0`
Solution
`("a" + 1/"a")^2 = 3`
⇒ `"a" + (1)/"a" = sqrt(3)`
Now, `("a" + 1/"a")^3`
= `"a"^3 + (1)/"a"^3 + 3("a" + 1/"a")`
⇒ `(sqrt(3))^3`
= `"a"^3 + (1)/"a"^3 + 3(sqrt(3))`
⇒ `"a"^3 + (1)/"a"^3`
= `3sqrt(3) - 3sqrt(3)`
= 0.
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