Question

If a, b, c, d are in continued proportion, prove that 3a-7d/7a+3d=3a^3-7b^3/7a^3+3b^3

please help

Answer 1

we know that

$\bold{ \frac{a}{b} = \frac{b}{c} = \frac{c}{d} = k, \: \: then}$

$\bold{a = bk = {ck}^{2} = {dk}^{3} and \: b = ck = {dk}^{2} \: \: and \: \: c = dk }$

$j$

$j$

$j$

L.H.S. =3a−4d2a+3d=3dk3−4d2dk3+3d=3k3−42k3+3

R.H.S. =3a3−4b32a3+3b3=3d3k9−4d3k62d3k9+3d3k6=d3k6(3k3−4)d3k6(2k3+3)=3k3−42k3+3

∴ L.H.S. = R.H.S.