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Question
If m = `root(3)(15) and n = root(3)(14), "find the value of " m - n - 1/[ m^2 + mn + n^2 ]`
Solution
`root(3)(15) and n = root(3)(14)`
⇒ m3 = 15 and n3 = 14
∴ m - n - `1/(m^2 + mn + n^2)`
= `[(m^3 + m^2n + mn^2 ) - (m^2n + mn^2 + n^3 ) - 1]/[m^2 + mn + n^2 ]`
= `[ m^3 + m^2n + mn^2 - m^2n - mn^2 - n^3 - 1 ]/[m^2 + mn + n^2 ]`
= `[m^3 - n^3 - 1]/[ m^2 + mn + n^2 ]`
= `[ 15 - 14 - 1 ]/[ m^2 + mn + n^2 ]`
= `[ 1 - 1 ]/[ m^2 + mn + n^2 ]`
= 0
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