Question

If X=7+√5, find the value of X+(1/X)

Answer 1

Answer:

x =7+√5

1/x= 1/ 7+√5

Rationalising the denominator

1/x =1* (7-√5)/ (7+√5)*(7-√5)

1/x= 7-√5/ (7)^2 - (√5)^2

1/x= 7-√5 / 49-5

1/x= 7-√5 / 44

ATQ

x + 1/x = 7+√5 +( 7-√5/44)

x+1/x = (7+√5)*44 + 7-√5 / 44

x+1/x= 308 +44√5+ 7-√5/44

x+1/x= 315 +44√5-√5/44

Hope it helps you !!

Answer 2

Answer:

1/X= 1/7+√5

=1×7-√5/(7+√5)(7-√5)

=7-√5/49-5

=7-√5/44

X+(1/X)=7+√5+7-√5/44

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