Divide 28 into four parts in an A.P. so that the ratio of the producto – InterviewSolution

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