The product of 4 distinct +ve integers a,b,c,da,b,c,d is 8!8!. The numbers also satisfy ab+a+b+1=323 and bc+b+c+1=399ab+a+b+1=323andbc+b+c+1=399 then d=?

1 Answer
Jul 25, 2018

77.

Explanation:

We have, ab+a+b+1=323ab+a+b+1=323.

:. (a+1)(b+1)=17xx19...............(ast^1).

Similarly, from bc+b+c+1=399, we get,

(b+1)(c+1)=19xx21..................(ast^2).

Comparing (ast^1) and (ast^2), we can say that,

b+1=19, a+1=17 and c+1=21.

:. a=16, b=18, c=20.

:. d=(abcd)/(abc),

=(8!)/(16xx18xx20).

rArr d=7.

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