the sum of reciprocal of two consecutive odd natural numbers is 12/35 .Find those numbers
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The required numbers are 5 and 7
Step-by-step explanation:
Let the two consecutive odd natural numbers be *x* and *x+2*
According to question,
1/x + 1/x+2 = 12/35
→x+2+x/(x)(x+2) = 12/35
→35(2x+2) = 12(x²+2x)
→70x + 70 = 12x² + 24x
→12x² - 46x - 70 = 0
→6x² - 23x - 35 = 0
→6x² - 30x + 7x - 35 = 0
→6x(x-5) +7(x-5) = 0
→(x-5)(6x+7) = 0
→ x= 5, -7/6
We neglect x = -7/6 because it is not a natural number
Therefore the required numbers are 5 and 7
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