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 .
To solve for x in a tricky equation, you need to use algebraic methods such as factoring, substitution, or the quadratic formula. It is important to carefully follow the order of operations and to simplify the equation as much as possible before solving for x.
There is no one specific method for solving tricky equations. It is important to understand a variety of algebraic techniques and to use the method that best fits the equation at hand. Practice and familiarity with different methods will help you determine the most efficient approach.
The first step is to carefully read the equation and identify any patterns or terms that can be simplified or factored. Next, determine which algebraic method would be most effective, such as substitution, elimination, or the quadratic formula. Finally, solve for x by following the order of operations and checking your work.
To check if you have found the correct value for x, plug your solution back into the original equation and see if it satisfies the equation. If it does, then you have found the correct value for x. If it does not, then you may have made a mistake in your calculations and should recheck your work.
When solving equations with multiple variables, it can be helpful to isolate one variable at a time and simplify the equation as much as possible before moving on to the next variable. It may also be helpful to use substitution or elimination methods to eliminate variables and solve for the remaining variables.