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1) The number of ordered paurs of positive integer (m,n), such that 1/n + 1/m = 1/15

 

2) Consider the equation 2u + v + w + x + y + z = 3. How many solutions (u , v , w , x , y , z) of non-integers does this equation have?

Guest Oct 21, 2017
 #1
avatar+627 
+3

1) We can rewrite this as (n + m)/mn = 1/15, which also is mn = 15m + 15n.

 

We move everything to one side:

 

mn - 15m - 15n = 0 

 

There is this method of adding a special number to both sides to make this doable.

 

In this case, we do + ( - 225) to both sides. mn - 15m - 15n - 225 = -225 

 

We can rewrite this as -n*(m-15)-15(m-15)=-225, which also is (m-15)*(n-15) = 225

 

Using a factoring trick, 225 can be written as (1,225);(3,75);(5,45);(9,25);(15,15)

 

So there are nine ordered pairs because 15,15 is the same as 15,15. Others can be doubled. 

supermanaccz  Oct 21, 2017
 #3
avatar+90023 
+2

Very crafty.......!!!!!

 

I like this one.....!!!!

 

 

cool cool cool

CPhill  Oct 21, 2017
edited by CPhill  Oct 21, 2017
 #2
avatar+627 
+1

I am not sure with #2, can someone help me with that too?

supermanaccz  Oct 21, 2017

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