Question

when x=9+4root5 find rootx - 1/rootx

Answer 1

Given x = 9 + 4√5, find √x - 1 / √x

√x = √(9 + 4√5)

√x = √(√5 + √4 + 2√(5x4))

√x = √(√5 + √4)2  

√x = √5 + 2

1 / √x = 1 / (√5 + 2)  rationalize we get

1 / √x =  (√5 - 2)

∴ √x - 1 / √x = √5 + 2 - √5 + 2 = 4.

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