The discussion revolves around solving the equation a = x + 1/x for the variable x. Participants are exploring the implications of this equation and the methods to approach it.
The discussion is ongoing, with participants sharing their thoughts on the equation's structure and potential interpretations. There is a recognition of the need to avoid providing complete solutions, and some participants express concern about the level of detail in responses.
There is a mention of the importance of adhering to forum rules regarding homework help, particularly in relation to providing hints versus full solutions. The variable a is noted to potentially affect the nature of the roots of the resulting equations.
Multiplying both sides by x results in a quadratic equation.aaaa202 said:Homework Statement
find x in the equation:
a = x + 1/x
Homework Equations
The Attempt at a Solution
I sat down and thought it was easy to do, but was terribly schocked at the fact, that I didn't know how to solve this equation. What is the general approach?
If a ≠ 1, then [itex]\displaystyle a=\frac{x+1}{x}[/itex] does have one real root.HallsofIvy said:If that is 1= x+ (1/x) then multiplying both sides by x gives the quadratic equation [itex]x= x^2+ 1[/itex] which is equivalent to [itex]x^2- x+ 1= 0[/itex]. You will find that it has no real roots.
If it is, rather, 1= (x+ 1)/x (in which case you should have used parentheses) you can again multiply both sides by x to get x= x+ 1 which is not true for any value of x.
aaaa202 said:Homework Statement
find x in the equation:
a = x + 1/xHomework Equations
The Attempt at a Solution
I sat down and thought it was easy to do, but was terribly schocked at the fact, that I didn't know how to solve this equation. What is the general approach?
SammyS said:IMO: I think that since aaaa202 has not come back to post a response, we should probably not be giving a full-blown solution .