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If a, b, c, d are in GP, then (b+c)^(2)...

If `a, b, c, d ` are in GP, then `(b+c)^(2)`= ______.

A

`(b+d)(a+d)`

B

`(a+d)(c+d)`

C

`(a+b)(c+d)`

D

`(a+c)(b+d)`

Text Solution

Verified by Experts

The correct Answer is:
C
`a, b, c, d` are in GP
`a=a, b = ar, c =ar^(2), d=ar^(3)`
`b+c = ar + ar^(2) = ar (1+r)`
`(b+c)^(2) + a^(2)r^(2) (1+r^(2) + 2r)`
`= a^(2)r^(2) + a^(2)r^(4) + 2a^(2)r^(3)`
`= a*ar^(2) +ar*ar^(3) + a^(2r3) + a^(2r3)`
`= a*c +bd + bc +ad = a(c+ d ) + b(c+d)`
`= (a+b)(c+d)`
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