If a,b,c are in G.P., then ___.
a(b2+a2) = c(b2+c2)
a(b2+c2) = c(a2+b2)
a2(b+c) = c2(a+b)
b2=ac
If a,b,c are in G.P., then b2=ac.
⇒b2(a−c)=ac(a−c)
⇒b2a−b2c=a2c−ac2 ⇒b2a+ac2=a2c+b2c
⇒a(b2+c2)=c(a2+b2)
If a + b + c = 0, then prove the following
(a) (b + c) (b − c) + a(a + 2b) = 0
(b) a(a2 − bc) + b(b2 − ca) + c(c2 − ab) = 0
(c) a(b2 + c2) + b(c2 + a2) + c(a2 + b2) = −3abc
(d)