SOLUTION: the product of 3 consecutive even natural numbers divided by their sum is 64. what is the middle number?

Algebra.Com
Question 1012447: the product of 3 consecutive even natural numbers divided by their sum is 64. what is the middle number?

Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
the product of 3 consecutive even natural numbers divided by their sum is 64. what is the middle number?
----
1st:: 2x-2
2nd:: 2x
3rd:: 2x+2
-------
Equation:
2x(4x^2-4)/6x = 64
-------
4x^2-4 = 3*64
x^2 -1 = 3*16
x^2 = 49
x = 7 or x = -7
-------
1st:: 2x-2 = 12
2nd:: 14
3rd:: 16
---
OR
1st:: -16
2nd:: -14
3rd:: -12
===========
Cheers,
Stan H.
------------
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.
the product of 3 consecutive even natural numbers divided by their sum is 64. what is the middle number?
------------------------------------------------------------ 
Let x be that middle number.
Then the three numbers are (x-2), x, and (x+2).

Their product is P = (x-2)*x*(x+2) = x*(x^2 - 4).
Their sum is S = (x-2) + x + (x+2) = 3x.
The equation is 

 = 64,  or  = 64,  or   = 64.


 = 64*3 = 192,   = 192 + 4 = 196,  x = +/-14.

Since the condition talks about natural numbers, only positive value is the solution.

Answer. x = 14.


RELATED QUESTIONS

the product of 3 consecutive even natural numbers divided by their sum is 64. what is the (answered by stanbon,ikleyn)
. What is the largest natural number by which the product of three consecutive even... (answered by KMST)
sum of 3 consecutive even numbers is 24 .what is the middle... (answered by Seutip,Alan3354)
The product of three consecutive natural number is120. What is their... (answered by Alan3354)
there are 3 consecutive even intergers, the first number is divided by 4. the second is... (answered by ikleyn)
Find two consecutive even natural numbers such that the sum of their squares is 340 . (answered by Theo)
If the sum of 3 consecutive natural number is 1203, then what are the... (answered by math_helper)
The middle number of seven consecutive even numbers is 1004. What is the first number? (answered by Alan3354,stanbon)
the product of two consecutive even natural numbers is 48. find the numbers. (answered by richard1234,Alan3354)