If x = ( √(2a + 1) + √(2a − 1) ) / ( √(2a + 1) − √(2a − 1) ), prove that : x^2 − 4ax + 1 = 0.

Question

If  x = ( √(2a + 1) + √(2a − 1) ) / ( √(2a + 1) − √(2a − 1) ), prove that :  x^2 − 4ax + 1 = 0.

KnowledgeBoat · Accepted Answer

Given, Applying componendo and dividendo, we get : Squaring both sides, we get : Hence, proved that x2 - 4ax + 1 = 0.

Mathematics