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Question
If x = `1/[ 5 - x ] "and x ≠ 5 find "x^3 + 1/x^3`
Sum
Solution
Given x = `1/[ 5 - x ]`;
By cross multiplication
⇒ x(5 - x) = 1
⇒ x2 - 5x = -1
⇒ x2 + 1 = 5x
⇒ `[ x^2 + 1]/x = 5`
⇒ `[ x + 1/x ] = 5` ...(1)
We know that
`( x^3 + 1/x^3 ) = ( x + 1/x )^3 - 3( x + 1/x )`
= `(5)^3 - 3(5)` ...[From equation (1)]
= `x^3 + 1/x^3`
= 125 - 15
= 110
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