SOLUTION: What 2 numbers have a product of 128 and a sum of 48? I don't believe it has a solution with whole numbers anyway.

Question 375035: What 2 numbers have a product of 128 and a sum of 48?
I don't believe it has a solution with whole numbers anyway.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find these two numbers, we need to list all of the factors of .

Factors of :
1,2,4,8,16,32,64,128
-1,-2,-4,-8,-16,-32,-64,-128

Note: list the negative of each factor. This will allow us to find all possible combinations.

These factors pair up and multiply to .
1*128 = 128
2*64 = 128
4*32 = 128
8*16 = 128
(-1)*(-128) = 128
(-2)*(-64) = 128
(-4)*(-32) = 128
(-8)*(-16) = 128

Now let's add up each pair of factors to see if one pair adds to the middle coefficient :

First Number	Second Number	Sum
1	128	1+128=129
2	64	2+64=66
4	32	4+32=36
8	16	8+16=24
-1	-128	-1+(-128)=-129
-2	-64	-2+(-64)=-66
-4	-32	-4+(-32)=-36
-8	-16	-8+(-16)=-24

From the table, we can see that there are no pairs of numbers which add to .

So you are correct. There are no two rational numbers which multiply to 128 and add to 48.

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim

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