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If x^2- 5x +1=0 then , find the value of x^10 + 1 / x^5. kindly give the method of solving.

If x^2- 5x +1=0 then , find the value of


x^10 + 1 / x^5.


kindly give the method of solving.

Grade:

1 Answers

Abhinav R
19 Points
11 years ago

x^5  +  1/x^5 

 

Product of roots  ab = 1 => a=1/b

 

a^5  +  1/a^5  =  a^5 +  b^5 = ((5 + root(21) )^5)/32  +  ((5 - root(21))^5)/32

 

= (1/32) * [(5 + root(21))^5 + (5-root(21))^5]

 

Apply binomial expansion all even terms of each expansion gets cancelled and odd terms get doubled

 

= (2/32) * [ (1)(5)^5 + (10)(5)^3(21) + 5(5)(21)^2]

= (1/16)*[3125 + 26250 + 11025]

=40500/16

=10125/2

 

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