The complexity of x=y

Algebra Level 2

the graph $x=y$ looks like a diagonal line

what does the graph $x^n=y^n$ look like when $n$ is even

extra: try to not use a calculator

like a circle like a curve like a X like a diagonal line

1 solution

Bento Cheese
Aug 15, 2019

$x^n=y^n$

$\sqrt[n]{x^n}=\sqrt[n]{y^n}$

$x=y$ , therefore a curve of any kind (including circle) is out of the question since the equation is linear

since even exponents turn any negative number into a positive number $(-m)^2=m^2$ then $-1^2=1^2$

$1^2=1^2$

$-1^2=1^2$

$1^2=-1^2$

$-1^2=-1^2$

same for 2

$2^2=2^2$

$-2^2=2^2$

$2^2=-2^2$

$-2^2=-2^2$

therefore, the answer is that it looks like an X