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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.
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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