Question Number 178180 by mathlove last updated on 13/Oct/22
$${x}+\frac{\mathrm{1}}{{x}}=−\mathrm{1}\:\:\:\:\:\:\:\:\:\:{x}^{\mathrm{1377}} =? \\ $$
Commented by saboorhalimi last updated on 13/Oct/22
Answered by saboorhalimi last updated on 13/Oct/22
$$\mathrm{check}\:\mathrm{out}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{which} \\ $$$$\mathrm{I}\:\mathrm{proposed}\: \\ $$
Commented by Acem last updated on 14/Oct/22
$${Very}\:{good}! \\ $$
Answered by Rasheed.Sindhi last updated on 14/Oct/22
$${x}^{\mathrm{2}} =−{x}−\mathrm{1} \\ $$$${x}^{\mathrm{3}} =−{x}^{\mathrm{2}} −{x}=−\left(−{x}−\mathrm{1}\right)−{x}=\mathrm{1} \\ $$$${x}^{\mathrm{1377}} =\left({x}^{\mathrm{3}} \right)^{\mathrm{459}} =\mathrm{1}^{\mathrm{459}} =\mathrm{1} \\ $$
Commented by mathlove last updated on 14/Oct/22
$${thanks} \\ $$