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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