SOLUTION: The sum of a number and its reciprocal is 37/6. Find the number.

Algebra ->  Sequences-and-series -> SOLUTION: The sum of a number and its reciprocal is 37/6. Find the number.      Log On


   

Question 1156496: The sum of a number and its reciprocal is 37/6. Find the number.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let's a number be x
then and its reciprocal is 1%2Fx
if the sum of a number and its reciprocal is 37%2F6, we have
x%2B1%2Fx=37%2F6
%28x%5E2%2B1%29%2Fx=37%2F6 .....cross multiply
6%28x%5E2%2B1%29=37x
6x%5E2%2B6=37x
6x%5E2-37x%2B6=0.......use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-37%29+%2B-+sqrt%28%28-37%29%5E2-4%2A6%2A6+%29%29%2F%282%2A6%29+
x+=+%2837+%2B-+sqrt%281369-144+%29%29%2F12+
x+=+%2837+%2B-+sqrt%281225+%29%29%2F12+
x+=+%2837+%2B-+35%29%2F12+
solutions:
x+=+%2837+%2B+35%29%2F12+=>x+=+72%2F12+=>x+=+6
or
x+=+%2837+-+35%29%2F12+=>x+=+2%2F12+=>x+=+1%2F6

so, your number is +6 and its reciprocal is +1%2F6
or your number is +1%2F6 and its reciprocal is +6




Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!

The sum of a number and its reciprocal is 37/6. Find the number.
Let the numbers be N

Then we get: matrix%281%2C3%2C+N+%2B+1%2FN%2C+%22=%22%2C+37%2F6%29

matrix%281%2C3%2C+6N%5E2+%2B+6%2C+%22=%22%2C+37N%29 ------ Multiplying by LCD, 6N



6N(N - 6) - 1(N - 6) = 0

(6N - 1)(N - 6) = 0

6N - 1 = 0           or           N - 6 = 0

highlight_green%28matrix%281%2C7%2C+N%2C+or%2C+number%2C+%22=%22%2C+1%2F6%2C+or%2C+6%29%29