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If a,b,c are in A.P., then a^(3)+c^(3)-8...

If a,b,c are in A.P., then `a^(3)+c^(3)-8b^(3)` is equal to

A

2 abc

B

3abc

C

4abc

D

`-6 abc `

Text Solution

Verified by Experts

The correct Answer is:
D
2b=a+c
`rArr8b^(3)=(a+c)^(3)=a^(3)+c^(3)+3ac(a+c)`
or `8b^(3)=a^(3)+c^(3)+3ac(2b)`
or `a^(3)+c^(3)-8b^(3)=-6abc`
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Knowledge Check

  • If a,b,c are in A.P., then a^2(b+c)+b^2(c+a)+c^2(a+b) is equal to

    A
    `2/9(a+b+c)^3`
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    C
    `3/10(a+b+c)^3`
    D
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  • If a+b+c=8 and ab +bc +ca =12 , then a^(3) +b^(3) +c^(3) -3abc is equal to :

    A
    a) 144
    B
    b) 400
    C
    c) 224
    D
    d) 192

  • If a, b, c, d, e, f are in A.P., then e – c is equal to

    A
    2(c – a)
    B
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    C
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    D
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