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There are two sets A and B each of which consists of three numbers in A.P.whose sum is 15 andwhere D and d are the common differences such that D-d=1. If p/q=7/8, where p and q are the product of the numbers ,respectively, andd gt 0 in the two sets . The sum of the products of the numbers is set A taken two at at time is |
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Answer» 51 3a=3b=15 or a=b=5 Set A = {5-D,5,5+D} set B = {5-d,5,5+d} where D=d+1 ALSO, `p/q=(5(25-D^(2)))/(5(25-d^(2)))=7/8` `rArr25(8-7)=8(d+1)^(2)-7d^(2)` `rArrd=-17,1` but `dgt0rArrd=1` So, the numbers in set A are 3,5,7 and the nnumbers in set are 4,5,6. Now, sum of PRODUCT of numbers in set are 4,5,6. Now, sum of product of numbers in set A taken two at a TIME is `3xx5+3xx7+5xx7=71`. The sum of product ofnumbers in set B taken two at a time is `4xx5+5xx6+6xx4=74`. Also, `p=3xx5xx7=105 and q=4xx5xx6=120` `rArrq-p=15` |
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