If x = ( ³√(m + 1) + ³√(m − 1) ) / ( ³√(m + 1) − ³√(m − 1) ), prove that x^3 − 3x^2 m + 3x − m = 0.

Question

If  x = ( ³√(m + 1) + ³√(m − 1) ) / ( ³√(m + 1) − ³√(m − 1) ), prove that  x^3 − 3x^2 m + 3x − m = 0.

KnowledgeBoat · Accepted Answer

Given, Applying componendo and dividendo, we get : Cubing both sides, we get : Hence, proved that x3 - 3x2m + 3x - m = 0.

Mathematics