# If M = Root(3)(15) and N = Root(3)(14), "Find the Value of " M - N - 1/ M^2 + Mn + N^2 - Mathematics

Sum

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

Concept: Solving Exponential Equations
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#### APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (C) | Q 12 | Page 101