Question

ANSWER HERE - ✌️

The sum of reciprocal of three consecutive natural numbers be ‘y’ and product of the numbers

be ‘x’. If xy = a, then find the sum of product of three given number taken two at a time.

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Answer 1

Step-by-step explanation:

Let three consecutive natural numbers be n-1, n and n+1.

So, sum of reciprocals is y.

$\frac{1}{n - 1} + \frac{1}{n} + \frac{1}{n + 1} = y$

Also, product of numbers is 'x'.

So

$(n - 1)(n)(n + 1) = x$

It is also given that xy=a.

Now,

$\frac{1}{n - 1} + \frac{1}{n} + \frac{1}{n + 1} = y \\ \frac{n(n +1 ) + (n + 1)(n - 1) + n(n - 1)}{(n - 1)n(n + 1)} = y$

In this, the sum of product of three numbers taken two at a time is nothing but the numerator.

So, by cross multiplying, it's value is

$y \times (n - 1)n(n + 1)$

Again, their product is given as x.

So, the required answer is y × x which is also given as a.

The final answer is a.

Thank you