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

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Question 187058: The sum of a number and its reciprocal is 10/3. What is the number?
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 quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%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+=+%2810+%2B-+sqrt%28+100+-+36+%29%29%2F6+
x+=+%2810+%2B-+sqrt%28+64+%29%29%2F6+
x+=+%2810+%2B-+8%29%2F6+
x+=+3
x+=+1%2F3
The sum of 3 and it's reciprocal is 10/3
also, the sum of 1/3 and it's reciprocal is 10/3