Question 1045390: A number added to thrice its reciprocal is equal to 13/2. what is the number? Found 2 solutions by ikleyn, KMST:Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website! .
A number added to thrice its reciprocal is equal to 13/2. what is the number?
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= . <--- Multiply by 2x both sides.
= .
Apply the quadratic formula.
= = .
= 6; = .
Answer. The numbers are 6 and .
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website! There is nothing that says that the number is a positive integer,
but if that had been meant,the fifth grader approach would work well.
Otherwise, we could use the algebra approach.
THE FIFTH GRADER APPROACH:
It cannot be a very small number, like ,
because the sum would be too low.
It cannot be or more,
because the sum would be more than .
It must be a multiple of ,
because the sum has a in the denominator.
Could the number be ?
Its reciprocal is , and the sum i .
That is not .
The sum is less than ,
and obviously the bigger the starting number,
the larger the sum will be,
so let's try .
The reciprocal of is 1 ,
and the sum of plus thrice its reciprocal is .
So, the number is .
THE ALGEBRA APPROACH: = the mystery number, and = its reciprocal, so we know that .
Then, = the mystery number added to thrice its reciprocal.
The problem say that sum is , so our equation is .
Solving:
1
We multiply both sides of the equal sign in that equation times .
Since we now that , we know we get an equivalent equation.
We can solve that equation by factoring,
by completing the square,
or by using the quadratic formula,
to get the solutions and .