Thank you for reporting, we will resolve it shortly
Q.
If $x, y, z$ are in G.P. then $x^2+y^2, x y+y z, y^2+z^2$ are in-
Sequences and Series
Solution:
$x , y , z$ are in G.P.
$\therefore y^2=x z .....$(i)
$\Rightarrow x(x+z), y(x+z), z(x+z) $ are in G.P.
$\Rightarrow x^2+x z, x y+y z, z^2+x z $ are in G.P.
$\Rightarrow x^2+y^2, x y+y z, y^2+z^2$ are in G.P.
[putting $y^2=x z$ from (i)]