SOLUTION: A natural number, when increased by 3, equals 70 times its reciprocal. Find the number

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: A natural number, when increased by 3, equals 70 times its reciprocal. Find the number      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 953625: A natural number, when increased by 3, equals 70 times its reciprocal. Find the number
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
A natural number, when increased by 3, equals 70 times its reciprocal. Find the number
n=the number
n%2B3=70%281%2Fn%29
n%2B3=70%2Fn Multiply each side by n.
n%5E2%2B3n=70 Subtract 70 from each side.
n%5E2%2B3n-70=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation an%5E2%2Bbn%2Bc=0 (in our case 1n%5E2%2B3n%2B-70+=+0) has the following solutons:

n%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=%283%29%5E2-4%2A1%2A-70=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+289+%29%29%2F2%5Ca.

n%5B1%5D+=+%28-%283%29%2Bsqrt%28+289+%29%29%2F2%5C1+=+7
n%5B2%5D+=+%28-%283%29-sqrt%28+289+%29%29%2F2%5C1+=+-10

Quadratic expression 1n%5E2%2B3n%2B-70 can be factored:
1n%5E2%2B3n%2B-70+=+1%28n-7%29%2A%28n--10%29
Again, the answer is: 7, -10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-70+%29

ANSWER: The number is 7.
CHECK:
7+3=70(1/7)
10=70/7
10=10