Divide 20 into four parts which are in ap
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divide 20 into four parts which are in AP such that the product of the first and fourth is to the product of the second and third is 2:3
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:-)
let the four numbers to be the a-3d ,a-d, a+d ,a+3d as the numbers are in arithmetic progressions with common difference: 2d and (a-3d) +(a-d)+(a+d) +(a+3d)=20 we get 4a=20 a=5 (a-3d)(a+3d)/(a+d)(a-d)=2/3 (a-3d)(a+3d)*3=(a+d)(a-d)*2 i.e. 3a^2-27d^2=2a^2-2d^2 a^2=25d^2 :now substitute a=5 we get 25=25d^2 d^2=1 d=+1,-1 so the numbers become 2,4,6,8
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