(v) (a + 2b + 2c) (a – 2b + 2c) = a2 + 4c2
Solution:
(v) (a + 2b + 2c) (a – 2b + 2c) = a2 + 4c2
According to the question, a, b, c are in GP.
Making use of the property of geometric mean,
b2 = ac
Let us take the LHS: (a + 2b + 2c) (a – 2b + 2c)
(a + 2b + 2c) (a – 2b + 2c) = a2 – 2ab + 2ac + 2ab – 4b2 + 4bc + 2ac – 4bc + 4c2
= a2 + 4ac – 4b2 + 4c2
= a2 + 4ac – 4(ac) + 4c2 [Since, b2 = ac]
= a2 + 4c2
= RHS
∴ LHS = RHS
Hence proved.