Question

plz solve this problem ASAP

I'll mark the right answer as BRAINLIEST and spams will be reported​

Answer 1

$\huge \fbox \pink{Solution:}$

$\text{Let Be the common of the \:G.P. }$

$a ,b ,c ,d ,\text{ Then} ,b = ar ,c = {ar}^{2} \text{ and} \: d = {ar}^{3}$

$∴LHS = (b - c {)}^{2} + (c - a {)}^{2} + (d - b {)}^{2}$

$= (ar - {ar}^{2} {)}^{2} + ( {ar}^{2} - a {)}^{2} + ( {ar}^{3} - ar {)}^{2}$

$= {a}^{2} {r}^{2} (1 - r {)}^{2} + {a}^{2} ( {r}^{2} - 1 {)}^{2} {a}^{2} {r}^{2} ( {r}^{2} - 1 {)}^{2}$

$= {a}^{2} ( {r}^{6} - 2 {r}^{3} + 1)$

$= {a}^{2} (1 - {r}^{3} {)}^{2}$

$= (a - a {r}^{3} {)}^{2}$

$= (a - b {)}^{2}$

$\\ \\ \\ \\ \sf \colorbox{gold} {\red(ANSWER ᵇʸ ⁿᵃʷᵃᵇ⁰⁰⁰⁸}$