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प्रश्न
If `a + 1/a` = p and a ≠ 0; then show that:
`a^3 + 1/a^3 = p(p^2 - 3)`
उत्तर
Given that `a + 1/a` = p ...(1)
`(a + 1/a )^3 = a^3 + 1/a^3 + 3( a + 1/a )`
⇒ `a^3 + 1/a^3 = ( a + 1/a )^3 - 3( a + 1/a )`
⇒ `a^3 + 1/a^3 = (p)^3 - 3(p)` ...[From(1)]
⇒ `a^3 + 1/a^3 = p(p^2 - 3)`
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