SOLUTION: Find two positive real numbers that differ by 2 and have a product of 10

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Question 286544: Find two positive real numbers that differ by 2 and have a product of 10
Found 2 solutions by richwmiller, Fombitz:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
a-b=2
a*b=10
a=2+b
(2+b)*b=10
2b+b^2=10
b^2+2b-10=0
b=2.31662
a=4.31662
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ab%5E2%2Bbb%2Bc=0 (in our case 1b%5E2%2B2b%2B-10+=+0) has the following solutons:

b%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=%282%29%5E2-4%2A1%2A-10=44.

Discriminant d=44 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+44+%29%29%2F2%5Ca.

b%5B1%5D+=+%28-%282%29%2Bsqrt%28+44+%29%29%2F2%5C1+=+2.3166247903554
b%5B2%5D+=+%28-%282%29-sqrt%28+44+%29%29%2F2%5C1+=+-4.3166247903554

Quadratic expression 1b%5E2%2B2b%2B-10 can be factored:
1b%5E2%2B2b%2B-10+=+1%28b-2.3166247903554%29%2A%28b--4.3166247903554%29
Again, the answer is: 2.3166247903554, -4.3166247903554. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-10+%29

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
X%28X%2B2%29=10
X%5E2%2B2X=10
X%5E2%2B2X-10=0
Use the quadratic formula,
X+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
X+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-10%29+%29%29%2F%282%2A1%29+
X+=+%28-2+%2B-+sqrt%28+4%2B40+%29%29%2F%282%29+
X+=+%28-2+%2B-+sqrt%28+44+%29%29%2F%282%29+
X+=+%28-2+%2B-+2%2Asqrt%28+11+%29%29%2F%282%29+
Since only positive numbers are acceptable,
X+=+-1+%2B+sqrt%28+11+%29+
or approximately the two numbers are,
X=2.317
X+2=4.317
X(X+2)=10.002