Question

the product of four distinct +ve integers a,b,c, and d is 40320 the no. also satisfy for ab+ a+b =322 and bc+b+c=398 find d

Answer 1

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Answer 2

Answer:

$First\ equation:\\ab+a+b=322\\ab+a+b+1=323\\Which\ is\ equal\ to:\\(a+1)(b+1)=17*19...(i)\\\\Similarly,\\(b+1)(c+1)=19*21... (ii)\\Here, we\ see\ that\ (b+1)\ and\ 19\ are\ same\ in\ both\ the\ equations\\So, (b+1)=19, and\ b=18\\And,\\a = 16\\c=20\\so,\\abcd=40320\\16*18*20*d=40320\\and, d=7$

Hence, d = 7