the reciprocal of the product of the two consecutive integers is 1/30. find the two integers.?

Answer 1

5 and 6

Answer 2

Let x = one of the integers.
Since the integers in question are consecutive, it follows that
x + 1 is the other integer.

We know that the product of these two integers would be x(x + 1). It follows that the reciprocal of the product would be 1/[x(x + 1)].

Therefore,

1/[x(x +1)] = 1/30

Take the reciprocal of both sides, to obtain

x(x + 1) = 30

Expand the left hand side,

x^2 + x = 30

Now, move the 30 over to the left hand side,

x^2 + x - 30 = 0

Factor, to get

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

Therefore, x = {-6, 5}

Thus, you have TWO sets of consecutive numbers:
{-6, -5} and {5, 6}

Answer 3

Suppose that the first integer is x. Then the second integer is x+1. Now we have 1/(x(x+1)) = 1/30.
Therefore x(x+1) = 30 or x^2 + x - 30 = 0. This is equivalent with (x + 6)(x - 5) = 0.
Hence there are 2 answers : 5 and 6, or -6 and -5.
Hope that helps.

Answer 4

Let the integers be x and x + 1. Thus,

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

Then we get the reciprocal of both sides.
x(x + 1) = 30

Distribute x and transpose 30
x² + x - 30 = 0

Then, factor
(x + 6)(x - 5) = 0

Thus,
x + 6 = 0 or x - 5 = 0

Then
x = -6 or x = 5
x + 1 = -5 or x = 6

Therefore, the integers can be -6 and -5 or 5 and 6.

^_^

Answer 5

5 and 6

Answer 6

5 and 6

Answer 7

1/(x(x+1)) = 1/30
x(x+1) = 30
x^2 + x = 30
x^2 + x -30 = 0
factor... (x-5)(x+6)
x=5 or x=-6 will do...
so.. the two consecutive integer may be:
5 and 6, or
-6 and -5.

Math assignment?

Answer 8

let 1 of the integer be x,

then 1/(x*(x+1))= 1/30

thus, x*(x+1)=30
x^2+x-30=0
thus, solving it we get,
x=5 or x= -6
thus the integers can be (5,6) or (-6,-5)

Answer 9

5 and 6, clearly:

5 x 6 = 30; the reciprocal of that is 1/30. QED

Live long and prosper.