Given two CT signals $x_1(t)$ (even signal) and $x_2(t)$ (odd signal). If $x_1(t)+x_2(t)$ is an even signal then what is the energy and power of $x_2(t)$.
My Attempt
$\int \limits _{-\infty}^{+\infty}$ $\left| x_1(t)+x_2(t)\right|^2 dt$
Since the functions are real we can
= $\int \limits _{-\infty}^{+\infty}$ $\left( x_1(t)+x_2(t)\right)^2 dt$
= $\int \limits _{-\infty}^{+\infty}$ $x_1^2(t)dt$ + $\int \limits _{-\infty}^{+\infty}$ $x_2^2(t)dt$ + $\int \limits _{-\infty}^{+\infty}$ $2 x_1(t) x_2(t)dt$
This one was useful for the next step
= $\int \limits _{-\infty}^{+\infty}$ $x_1^2(t)dt$ + $\int \limits _{-\infty}^{+\infty}$ $x_2^2(t)dt$
Now the energy of $x_2(t)$ is the difference between the energy of $x_1(t) +x_2(t)$ and that of $x_1(t)$.
We know that $x_1(t)$ is even , $x_1(t)+x_2(t) $ is even , $x_2(t) $ is odd (however its energy function $x_2(t)^2$ is even since its product of two odds)
~~ And I'm stuck here ~~~
