Question

if x y and z are in continued proportion prove that xyz(x+y+z)^3=(xy+yz+zx)^3

Answer 1

$\huge \sf {\orange {\underline {\pink{\underline {♡A᭄ɴsᴡᴇʀ࿐ \ :- }}}}}$

x,y,z are in continued proportion, that is

yx=zy .... (1)

then,y2=xz

Now,(y+z)2(x+y)2  =z2(zy+1)2y2(yx+1)2

=z2(yx+1)2y2(yx+1)2              ( from (1)  yx=zy )

=z2y2

=z2xz

=z

Answer 2

$\huge{ \color{red}{ \textsf{ \textbf{ \underline{ \: \: αиѕωєя \: \: }}}}}$

x,y,z are in continued proportion, that is

yx=zy .... (1)

then,y2=xz

Now,(y+z)2(x+y)2  =z2(zy+1)2y2(yx+1)2

=z2(yx+1)2y2(yx+1)2              ( from (1)  yx=zy )

=z2y2

=z2xz

=z