SOLUTION: The sum of a number and its reciprocal is 10/3. Find the numbers

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: The sum of a number and its reciprocal is 10/3. Find the numbers      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1112826: The sum of a number and its reciprocal is 10/3. Find the numbers
Found 2 solutions by Alan3354, josmiceli:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of a number and its reciprocal is 10/3.
Find the numbers --- Not numbers. Just 1 number.
-----------
n = the number
n+%2B+1%2Fn+=+10%2F3


Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x+%2B+1%2Fx+=+10%2F3+
Multiply both sides by +3x+
+3x%5E2+%2B+3+=+10x+
+3x%5E2+-+10x+%2B+3+=+0+
---------------------------
Use the quadratic formula
+x+=+%28+-b+%2B-sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29%2F+%282a%29+
+a+=+3+
+b+=+-10+
+c+=+3+
+x+=+%28+-%28-10%29+%2B-sqrt%28+%28-10%29%5E2+-+4%2A3%2A3+%29%29%2F+%282%2A3%29+
+x+=+%28+10+%2B-sqrt%28+100+-+36+%29%29%2F6+
+x+=+%28+10+%2B-sqrt%28+64+%29%29%2F6+
+x+=+%28+10+%2B+8+%29%2F6+
+x+=+3+
and
+x+=+%28+10+-+8+%29%2F6+
+x+=+1%2F3+
------------------------
The answers are 3, and 1/3