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Question
If \[\frac{a}{b} + \frac{b}{a} = - 1\] then a3 − b3 =
Options
1
-1
- \[\frac{1}{2}\]
0
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Solution
Given `a/b+b/a = -1`
Taking Least common multiple in `a/b +b/a = -1 `we get,
` a/b + b/a -1`
`(axx a)/(b xx a)+(bxxb)/(a xx b) = -1`
`a^2/(ab) + b^2/(ab) = -1`
`(a^2 + b^2)/(ab) = -1 `
`a^2+b^2 = -1 xx ab`
`a^2 +b^2 = -ab`
`a^2 + b^2 + ab = 0`
Using identity `a^3 - b^3= (a-b) (a^2 +ab +b^2)`
`a^3 -b^3 = (a-b)(a^2 + ab+b^2)`
`a^3 -b^3 = (a-b)(0)`
`a^3 - b^3 = 0`
Hence the value of `a^3 - b^2` is 0.
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