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Divide 28 into four parts in an A.P. so ...

Divide 28 into four parts in an A.P. so that the ratio of the product of first and third with the product of second and fourth is 8:15.

Text Solution

Verified by Experts

The correct Answer is:
4, 6, 8, 10
Let four member be a-3d,a-d,a+b,a+3d.
Here, 4a=28 or a=7
Also, `((a-3d)(a+d))/((a-d)(a+3d))=8/15`
or `15[a^(2)-3d^(2)-2ad]=8[a^(2)-3d^(2)+2ad]`
or `7(a^(2)-3d^(2))=46ad`
or `7(49-3d^(2))=46xx7xxd`
or `49-3d^(2)=46d`
`3d^(2)+46d-49=0`
or (d-1)(3d+49)=0
or d=1
Therefore, the required numbers are 4, 6, 8, 10.
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