SOLUTION: What two numbers have a product that is twice their sum and have a difference of 2

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Question 851006: What two numbers have a product that is twice their sum and have a difference of 2


Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
What two numbers have a product that is twice their sum and have a difference of 2

Solution:
Let one number be x. Then the other is x + 2.
Sum of the numbers = x+%2B+x+%2B+2+=+2%2Ax+%2B+2
Product = x%2A%28x+%2B+2%29+=+x%5E2+%2B+2%2Ax
Since product is twice the sum,

x%5E2+%2B+2%2Ax+=+2%282%2Ax+%2B+2%29+=+4%2Ax+%2B+4

x%5E2+-+2%2Ax+-+4+=+0

Solution below:

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%2B-4+=+0) has the following solutons: x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number. First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-2%29%5E2-4%2A1%2A-4=20. Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+20+%29%29%2F2%5Ca. x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+3.23606797749979 x%5B2%5D+=+%28-%28-2%29-sqrt%28+20+%29%29%2F2%5C1+=+-1.23606797749979 Quadratic expression 1x%5E2%2B-2x%2B-4 can be factored: 1x%5E2%2B-2x%2B-4+=+1%28x-3.23606797749979%29%2A%28x--1.23606797749979%29 Again, the answer is: 3.23606797749979, -1.23606797749979. Here's your graph: graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-4+%29
The 2 numbers are approximately highlight%283.23%29 and highlighthighlight%285.23%29 Hope this helps :)