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Question
If `"m"^2 + (1)/"m"^2 = 51`; find the value of `"m"^3 - (1)/"m"^3`
Solution
`"m"^2 + (1)/"m"^2 = 51`
We know that
`("m" - 1/"m")^2`
= `"m"^2 + (1)/"m"^2 - 2`
⇒ `("m" - 1/"m")^2` = 51 - 2
⇒ `("m" - 1/"m")^2` = 49 = 72
⇒ `"m" - 1/"m"` = 7
⇒ `("m" - 1/"m")^3` = 73
⇒ `"m"^3 - (1)/"m"^3 - 3("m" - 1/"m")` = 343
⇒ `"m"^3 - (1)/"m"^3 - 3 xx 7` = 343
⇒ `"m"^3 - (1)/"m"^3`
= 343 + 21
= 364.
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