Question

(

b-c)²+(c-a)²+(b-d)²=(a-d)²​

Answer 1

R.H.S=(b−c) 2 +(c−a) 2+(d−b) 2

Being a,b,c and d in GP,

ba = cb = dc

b 2=ac,c 2=bd and ac=bd, ad=bc,

RHS=b 2 +c 2−2bc+c 2+a 2 −2ac+d 2+b 2−2bd

=2b 2−2bc+2c 2+a 2−2b 2 +d 2−2c 2

=a 2 +d 2 −2ad

=(a−d) 2

=LHS