The lcm and hcf of 2 consicutive even no. Is 84 & 2 .find the sum of reciprocal of sum.
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Product of numbers = Lcm×Hcf
Numbers are 2a, 2a+2
2a(2a+2)=84×2
a(2a+2)= 84×2/2
a2(a+1)= 84
2 a^2+2a-84=0
a^2+a-42=0
a^2+7a-6a-42=0
a(a+7)-6(a+7)= 0
(a+7)(a-6)= 0
a=6,-7
a=6 is considered
Numbers are
2a=2(6)= 12
2a+2
2(6)+2=14
12,14 are numbers
Sum = 12+14== 16
Reciprocal sum
1/12+1/14
7+6/84
13/84
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