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Two consecutive integers: x, (x+1)

Reciprocals = 1/x , 1/(x+1)

Sum of reciprocals = 11/30

1/x + 1/(x+1) = 11/30

Multiply equation by 30x(x+1) and you have:

= 30x + 30(x+1) = 11x(x+1)

= 30x + 30x+30 = 11x^2 + 11x

= 60x+30 = 11x^2+11x

0 = 11x^2+11x-60x-30

So, this is a quadratic equation. We can simplify the expression further.

11x^2+11x-60x-30 = 0

11x^2 - 49x - 30 = 0

Now, the factors of the expression are :

=(11x + 6)((x - 5) = 0

In (x-5), we can say 5 is the integral solution and therefore,

**x = 5**

So, the first number is 5

The second number = x+1 = 5+1

**= 6**

**The two numbers = 5,6**

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### This Is a Certified Answer

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**Let The Number be x and x + 1**

**According To Given Statement**

1 + 1 = 11

--- ------ -----

x x + 1 30

x + 1 + x = 11

------------ ------

x² + x 30

60x + 30 = 11x² + 11x

11x² + 11x - 60x - 30 = 0

11x² - 49x- 30 = 0

11x² - 55x + 6x - 30 = 0

11x(x - 5) +6(x - 5) = 0

(11x + 6)(x - 5) = 0

**x = -6/11 OR x = 5**

**Therefore the first No . is 5 as -6/11 is Not a Natural No.**

**So ,**

**Second Natural No = 6**

**So the Numbers are 5 and 6**

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