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प्रश्न
If `"a"^2 + (1)/"a"^2 = 14`; find the value of `"a"^3 + (1)/"a"^3`
उत्तर
Using (a + b)2 = a2 + 2ab + b2
`("a" + 1/"a")^2`
= `"a"^2 + 2"a"(1/"a") + (1/"a")^2`
⇒ `("a" + 1/"a")^2 = "a"^2 + 2 + (1)/"a"^2`
⇒ `("a" + 1/"a")^2 = "a"^2 + (1)/"a"^2 + 2`
⇒ `("a" + 1/"a")^2` = 14 + 2
⇒ `("a" + 1/"a")^2` = 16
⇒ `"a" + (1)/"a"` = ±4
`"a"^3 + (1)/"a"^3`
= `("a" + 1/"a")("a"^2 + 1/"a"^2 - 1)` ....[Using a3 + b3 = (a + b)(a2 + b2 - ab)]
= (±4)(14 - 1)
= (±4)(13)
= ±52.
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