Question 1175013: the sum of a number and its reciprocal is 10/3. what is the number?
define the variable
thought process
equations
solving equation
answer
Answer by ikleyn(52777)   (Show Source):
You can put this solution on YOUR website! .
After reading your post, I turn on my mind.
 = 3  = 3 + .
So, the number is 3 and its reciprocal is . ANSWER
Solved.
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Wait a minute (!)
There is A N O T H E R solution, too, and you should know it:
Another answer is THIS: the number is and its reciprocal is 3.
Now all possible solutions are in place (!)
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Let me add something for your education.
This problem can be solved formally.
This way goes through solving quadratic equation.
Other people (and other teachers) consider such problems as "joke" problems,
that can be solved mentally in 3-4-5 seconds.
For advanced young students of 5-th grade level, who are able freely manipulate fractions,
it is a "joke" problem, which SHOULD be solved mentally, and it gives them fan to do it.
For other students, the formal way is often very boring and torturing way to solve it formally.
The formal way is THIS :
Let x be the number; then reciprocal is  .
The equation is THIS:
x + = .
Multiply both sides by 3x
3x^2 + 3 = 10x
3x^2 - 10x + 3 = 0
 =  =  =  .
One root is  =  =  = 3.
The other root is  =  =  = .
Thus we solved the problem formally and obtained BOTH solutions (!)
. . . . . . .
Good student should know both ways.
Worst or better, the average student will, probably, learn the hard way in the school.
But I am 129% sure that NOBODY and NEVER will show him (or her) the easy way.
But without knowing this easy way, Math education can not be considered as complete.
Therefore, I started with this easy "joking" mode.
Happy learning (!)
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