Question 86
Find all the $(x, y, z)$ triplets of real numbers which are solution of the equation $$
\sqrt{3^{x}\left(5^{y}+7^{z}\right)}+\sqrt{5^{y}\left(7^{z}+3^{x}\right)}+\sqrt{7^{z}\left(3^{x}+5^{y}\right)}=\sqrt{2}\left(3^{x}+5^{y}+7^{z}\right)
$$
\sqrt{3^{x}\left(5^{y}+7^{z}\right)}+\sqrt{5^{y}\left(7^{z}+3^{x}\right)}+\sqrt{7^{z}\left(3^{x}+5^{y}\right)}=\sqrt{2}\left(3^{x}+5^{y}+7^{z}\right)
$$