Question

If m = `root(3)(15) and n = root(3)(14), "find the value of " m - n - 1/[ m^2 + mn + n^2 ]`

Answer 1

`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