Q. 9 B

# If a, b, c, d are

Answer :

a, b, c, d are in G.P.

Therefore,

bc = ad … (1)

b2 = ac … (2)

c2 = bd … (3)

If somehow we use RHS and Make it equal to LHS, our job will be done.

we can manipulate the RHS of the given equation as –

Note: Here we are manipulating RHS because working with a simpler algebraic equation is easier and this time RHS is looking simpler.

RHS = (a + b)2 + 2(b + c)2 + (c + d)2

RHS = a2 + b2 + 2ab + 2(c2 + b2 + 2cb) + c2 + d2 + 2cd

RHS = a2 + b2 + c2 + d2 + 2ab + 2(c2 + b2 + 2cb) + 2cd

Put c2 = bd and b2 = ac, we get –

RHS = a2 + b2 + c2 + d2 + 2(ab + ad + ac + cb + cd)

You can visualize the above expression by making separate terms for (a + b + c)2 + d2 + 2d(a + b + c) = {(a + b + c) + d}2

RHS = (a + b + c + d)2 = LHS

Hence Proved.

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