If frac{{x + y}}{2},;y,;frac{{y + z}}{2} are | vedclass

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Question

(b) If $\frac{{x + y}}{2},\;y,\;\frac{{y + z}}{2}$ are in $H.P.$, then

$y = \frac{{xy + xz + {y^2} + yz}}{{x + 2y + z}}$

$ \Rightarrow $ $xy + 2

Vedclass · Accepted Answer

$G.P.$

Vedclass · Answer

(b) If $\frac{{x + y}}{2},\;y,\;\frac{{y + z}}{2}$ are in $H.P.$, then

$y = \frac{{xy + xz + {y^2} + yz}}{{x + 2y + z}}$

$ \Rightarrow $ $xy + 2{y^2} + yz = xy + xz + {y^2} + yz$

$ \Rightarrow $${y^2} = xz$

Thus $x,\;y,\;z$ will be in $G.P.$

If $\frac{{x + y}}{2},\;y,\;\frac{{y + z}}{2}$ are in $H.P.$, then $x,\;y,\;z$ are in

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