SOLUTION: 1.)A number less its reciprocal is 8/3.what is the number? 2.)IF A NUMBER IS SUBTRACTED FROM TWICE,ITS RECIPROCAL.THE RESULT IS -23/5.WHAT IS THE NUMBER?

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Question 162010: 1.)A number less its reciprocal is 8/3.what is the number?
2.)IF A NUMBER IS SUBTRACTED FROM TWICE,ITS RECIPROCAL.THE RESULT IS -23/5.WHAT IS THE NUMBER?

Answer by ankor@dixie-net.com(12701) About Me  (Show Source):
You can put this solution on YOUR website!
1.)A number less its reciprocal is 8/3.what is the number?
:
Just write an equation for what it says:
x - 1%2Fx = 8%2F3
Multiplying the equation by 3x gets rid of the denominators, results;
3x(x) - 3(1) = 8x
3x^2 - 3 - 8x = 0
3x^2 - 8x - 3; our old friend, the quadratic equation
factor is to:
(3x + 1)(x - 3) = 0
The positive solution:
x = 3
:
Check is in the original equation
3 - 1%2F3 = 8%2F3
9%2F3 - 1%2F3 = 8%2F3
:
What about the negative solution?
3x = -1
x = -1%2F3
This too, will work
-1%2F3 - 1%2F%28-1%2F3%29 = 8%2F3
-1%2F3 + 3 = 8%2F3
:
:

2.)IF A NUMBER IS SUBTRACTED FROM TWICE,ITS RECIPROCAL.THE RESULT IS -23/5.WHAT IS THE NUMBER?
:
2(1%2Fx) - x = -23%2F5
which is:
2%2Fx - x = -23%2F5
Multiplying equation by 5x gets rid of the denominators
5(2) - 5x(x) = -23x
10 - 5x^2 = -23x
Arrange as a quadratic equation:
0 = 5x^2 - 23x - 10
Factor this to:
(5x + 2)(x - 5) = 0
The positive solution:
x = +5
The negative solution
5x = -2
x = -2%2F5
;
I leave it to you to check these solutions in the original equation like we did in the 1st one.