Question

The sum of the reciprocals of 2 consecutive numbers is 15/56. Find the number ​

Answer 1

Answer:

Given->

x,y are consecutive no.s

So x, x+1 are consecutive as well.

Now,

1/x   +   1/x+1   =   15/56

Taking LCM

x+1+x  /  x^2+x =  15/56

102x+56=15x^2+15x

15x^2-87x-56=0

by middle term splitting we get

x=7

So the numbers are 7, 8

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Answer 2

Given,

The sum of the reciprocals of 2 consecutive numbers is 15/56.

To find,

Find the two consecutive numbers.

Solution,

Let the two consecutive numbers be x and x+1.

Then the reciprocal of two consecutive numbers x and x+1 would be 1/x and 1/(x+1) respectively.

According to the problem given,

1/x + 1/(x+1) = 15/56.

Now, we have to solve for the value of x.

⇒  $\frac{1}{x}+\frac{1}{(x+1)}=\frac{15}{56}$

⇒  $\frac{(x+1) + x}{x(x+1)}=\frac{15}{56}$

⇒   (2x+1)56 = 15(x²+x)

⇒   112x+56=15x²+15x

⇒   15x²+15x-112x-56=0

⇒   15x²-97x-56=0.

Solving the equation we would get two values of x = 7 and x =  -8/15.

• Hence, 7 and 8 i.e. x, x+1 are the two consecutive numbers that we have to find.

• We can verify our result as the sum of reciprocal of 7 and 8 is 15/56.

        $\frac{1}{7} +\frac{1}{8}=\frac{15}{56}$

So the numbers 7 and 8 i.e. x and (x+1) are two consecutive numbers whose sum of reciprocal is 15/56.