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If-x-1-2016-2-then-4x-3-2019x-2017-equals-




Question Number 111534 by Aina Samuel Temidayo last updated on 04/Sep/20
If x=((1+(√(2016)))/2), then  4x^3 −2019x−2017 equals?
$$\mathrm{If}\:\mathrm{x}=\frac{\mathrm{1}+\sqrt{\mathrm{2016}}}{\mathrm{2}},\:\mathrm{then} \\ $$$$\mathrm{4x}^{\mathrm{3}} −\mathrm{2019x}−\mathrm{2017}\:\mathrm{equals}? \\ $$
Answered by Lordose last updated on 04/Sep/20
  ★   −2
$$ \\ $$$$\bigstar\:\:\:−\mathrm{2} \\ $$
Answered by 1549442205PVT last updated on 04/Sep/20
4x^3 −2019x−2017=4×((1+3(√(2016))+3.2016+2016(√(2016)))/8)  −((2019+2019(√(2016)))/2)−2017  =((2019(√(2016))+6049−2019−2019(√(2016)))/2)−2017  =((4030)/2)−2017=2015−2017=−2
$$\mathrm{4x}^{\mathrm{3}} −\mathrm{2019x}−\mathrm{2017}=\mathrm{4}×\frac{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{2016}}+\mathrm{3}.\mathrm{2016}+\mathrm{2016}\sqrt{\mathrm{2016}}}{\mathrm{8}} \\ $$$$−\frac{\mathrm{2019}+\mathrm{2019}\sqrt{\mathrm{2016}}}{\mathrm{2}}−\mathrm{2017} \\ $$$$=\frac{\mathrm{2019}\sqrt{\mathrm{2016}}+\mathrm{6049}−\mathrm{2019}−\mathrm{2019}\sqrt{\mathrm{2016}}}{\mathrm{2}}−\mathrm{2017} \\ $$$$=\frac{\mathrm{4030}}{\mathrm{2}}−\mathrm{2017}=\mathrm{2015}−\mathrm{2017}=−\mathrm{2} \\ $$
Commented by Aina Samuel Temidayo last updated on 04/Sep/20
Thanks.
$$\mathrm{Thanks}. \\ $$

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