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Question Number 10078 by ridwan balatif last updated on 23/Jan/17

Commented by ridwan balatif last updated on 23/Jan/17

x_1 ^(2011) +x_2 ^(2011) =A and x_1 ^(2012) +x_2 ^(2012) =B where x_1 and x_2    is the roots of x^2 −2x−5=0, x_1 ^(2015) +x_2 ^(2015) =...?

$$\mathrm{x}_{\mathrm{1}} ^{\mathrm{2011}} +\mathrm{x}_{\mathrm{2}} ^{\mathrm{2011}} =\mathrm{A}\:\mathrm{and}\:\mathrm{x}_{\mathrm{1}} ^{\mathrm{2012}} +\mathrm{x}_{\mathrm{2}} ^{\mathrm{2012}} =\mathrm{B}\:\mathrm{where}\:\mathrm{x}_{\mathrm{1}} \mathrm{and}\:\mathrm{x}_{\mathrm{2}} \: \\ $$$$\mathrm{is}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} −\mathrm{2x}−\mathrm{5}=\mathrm{0},\:\mathrm{x}_{\mathrm{1}} ^{\mathrm{2015}} +\mathrm{x}_{\mathrm{2}} ^{\mathrm{2015}} =...? \\ $$

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