Question

if x= 9+4root5
find the value of root x-1/root x

Answer 1

Step-by-step explanation:

x = 9 + 4√5

So, 1/x = 1/(9 + 4√5)

1/x = (9 - 4√5) / (9 + 4√5)(9 - 4√5)

1/x = (9 - 4√5) / (9² - (4√5)²)

1/x = (9 - 4√5) / (81 - 80) = (9 - 4√5) / 1

1/x = (9 - 4√5)

According to question: √x - 1/√x

So, √x - 1/√x = [ (√x)² - 1 ] / √x

= (x - 1) / √x

= (x - 1) * (1/√x)

= (x - 1) * √(1/x)

= (9 + 4√5 - 1) * √(9 - 4√5)

Thanks!