SOLUTION: The sum of 2 numbers is 6 and their product is 4 find the larger of the 2 numbers

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Question 787186: The sum of 2 numbers is 6 and their product is 4 find the larger of the 2 numbers
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
x+%2B+y+=+6 ________ (1)
xy+=+4 ________ (2)

Substituting for y in terms of x from (2) into (1)
x+%2B+4%2Fx+=+6
x%5E2-6x%2B4=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B4+=+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=%28-6%29%5E2-4%2A1%2A4=20.

Discriminant d=20 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+20+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+20+%29%29%2F2%5C1+=+5.23606797749979
x%5B2%5D+=+%28-%28-6%29-sqrt%28+20+%29%29%2F2%5C1+=+0.76393202250021

Quadratic expression 1x%5E2%2B-6x%2B4 can be factored:
1x%5E2%2B-6x%2B4+=+1%28x-5.23606797749979%29%2A%28x-0.76393202250021%29
Again, the answer is: 5.23606797749979, 0.76393202250021. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B4+%29



The larger number is 5.24