Question

Show that a=x+1/x where x=((√a+2)+(√a-2))/((√a+2)-(√a-2))

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Answer 1

https://www.sarthaks.com/?qa=blob&qa_blobid=9795267962806245037

Show that a = x+1/x where x = ((√a+2) + (√a-2))/((√a+2)-(√a-2))

x = ((√a+2)+(√a-2))/((√a+2)-(√a-2))

Rationalizing ... 

x = ((√a+2)+(√a-2))/((√a+2)-(√a-2)) = (a+2 + a-2 + 2 (√a+2) (√a-2) )/(4) = (2a + 2 (√a+2) (√a-2) )/(4)

1/x =((√a+2)-(√a-2))/((√a+2)+(√a-2)) 

Rationalizing ... 

1/x = (a+2 + a-2 - 2 (√a+2) (√a-2) )/(4) = (2a - 2 (√a+2) (√a-2) )/(4) 

x + 1/x = (4a)/(4) = a