Question 1075739
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there are 3 positive whole numbers, the product of first and second number is 24, second and third number is 48, 
first and third number is 32. find the value of three number?
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There is much more elegant solution:


<pre>
xy = 24,    (1)
yz = 48,    (2)
xz = 32.    (3)

Multiply all three equations (both sides). You will get

{{{x^2*y^2*z^2}}} = 24*48*32,   or

xyz = +/- {{{sqrt(24*48*32)}}},   or

xyz = +/- {{{24*8}}} = +/- 192.   (4)


Now divide equation (4) by the equation (1) (both sides). You will get

z = +/- 8.


Next divide equation (4) by the equation (2) (both sides). You will get

x = +/- 4.


Finally, divide equation (4) by the equation (3) (both sides). You will get

y = +/- 6


<U>Answer</U>.  There are <U>TWO</U> solutions:  a) (x,y,z) = (4,6,8),   and   b) (x,y,z) = (-4,-6,-8).


         If you want the solution in positive numbers, then keep a).
</pre>

Solved.



<U>Lesson to learn from this solution</U>: This problem was designed with the only SPECIAL goal: in order for you learn THIS solution.