If x, y, z are in G.P. then x2+y2, x y+y z, y2+z2 are in-

Question

If x, y, z are in G.P. then x2+y2, x y+y z, y2+z2 are in- (A) A.P. (B) G.P. (C) H.P. (D) Decreasing order

Tardigrade Admin · Accepted Answer

x , y , z are in G.P. ∴ y2=x z .....(i) ⇒ x(x+z), y(x+z), z(x+z) are in G.P. ⇒ x2+x z, x y+y z, z2+x z are in G.P. ⇒ x2+y2, x y+y z, y2+z2 are in G.P. [putting y2=x z from (i)]

Q. If $x, y, z$ are in G.P. then $x^{2} + y^{2}, x y + yz, y^{2} + z^{2}$ are in-

A.P.

G.P.

H.P.

Decreasing order

$x, y, z$ are in G.P.
$∴ y^{2} = x z .....$ (i)
$\Rightarrow x (x + z), y (x + z), z (x + z)$ are in G.P.
$\Rightarrow x^{2} + x z, x y + yz, z^{2} + x z$ are in G.P.
$\Rightarrow x^{2} + y^{2}, x y + yz, y^{2} + z^{2}$ are in G.P.
[putting $y^{2} = x z$ from (i)]

Q. If x,y,z are in G.P. then x2+y2,xy+yz,y2+z2 are in-