2018 in Algebra (2)

Algebra Level 2

Solve according to the following: $xy=2018 \text{ and } x^2+y^2=2018 \implies x^4+y^4= - m^2$

what is the value of $m=?$

1 solution

Marta Reece
Mar 6, 2018

$x^2+y^2=2018$

$(x^2+y^2)^2=2018^2$

$x^4+2x^2y^2+y^4=2018^2$

$(x^4+y^4)+2(xy)^2=2018^2$

$(x^4+y^4)=2018^2-2(xy)^2$

$(x^4+y^4)=2018^2-2\cdot2018^2$

$(x^4+y^4)=-2018^2$

$m=\boxed{2018}$

It's clever, particularly since there is no real $x$ or $y$ , so that it cannot be first solved for those.

Marta Reece - 3 years, 3 months ago

Thank you.

Hana Wehbi - 3 years, 3 months ago