Question

if a b c d are in GP then prove that bc = ad​

Answer 1

b^2=ac

c^2=bd

then, b^2 × c^2 = abcd

bc×bc= ad×bc

bc=ad

Answer 2

★For Your Better Understanding I just give a picture which had another similar question★

(b-c)^2 + (c-a)^2 + (d-b)^2 = (a-d)^2

Let a = p, b = pr , c = pr² and d = pr³

Now, LHS = (b - c)² + (c - a)² + (d - b)²

= (pr - pr²)² + (pr² - p)² + (pr³ - pr)²

=( p²r² + p²r⁴ - 2p²r³) + (p²r⁴ + p² - 2p²r²) + (p²r^6 + p²r² -2p²r⁴)

= p²r^6 - 2p²r³ + p²

= (pr³) -2(pr³)(p) + p²

= (pr³ - p)²

= (p - pr³)²

=(a - d)² = RHS


HOPE IT HELPED ^_^