Question

x=3+2underroot2 find underroot x-1/underrootx

Answer 1

HELLO DEAR,



given that:-

x = (3 + 2√2)


NOW,


1/x = 1/(3 + 2√2) × (3 - 2√2)/(3 - 2√2)

1/x = (3 - 2√2)/(9 - 8)

1/x = (3 - 2√2)



NOW,


(√x - 1/√x)² = x + 1/x - 2√x * 1/√x

(√x - 1/√x)² = (3 + 2√2) + (3 - 2√2) - 2

(√x - 1/√x)² = 3 + 3 + 2√2 - 2√2 - 2

(√x - 1/√x)² = 6 - 2

(√x - 1/√x)² = 4

(√x - 1/√x) = 2



I HOPE ITS HELP YOU DEAR,
THANKS