Geometric Progressions — MATHS STD 11 Science — Question

$\therefore\text{b}^2=\text{ac }\cdots(1)$

$\text{L.H.S}=({\text{a}+\text{b}+\text{c}+\text{d})^2}$

$=(\text{a}+\text{b})^2+2(\text{a}+\text{b})(\text{c}+\text{d})+(\text{c}+\text{d})^2$

$=(\text{a}+\text{b})^2+2(\text{ac}+\text{ad}+\text{bc}+\text{bd})+(\text{c}+\text{d})^2$

$=(\text{a}+\text{b})^2+2(\text{b}^2+\text{bc}+\text{bc}+\text{c}^2)+(\text{c}+\text{d})^2$ $[\text{Using (1)}]$

$=(\text{a}+\text{b})^2+2(\text{b}+\text{c})^2+(\text{c}+\text{d})^2$

$=\text{R.H.S}$

$\therefore\text{R.H.S}=\text{L.H.S}$