x^3=5x
what is the largest possible value for x?
To find the largest possible value for x that satisfies the equation x^3=5x, we can start by rearranging the equation to get it in a form that makes it easier to solve.
x^3 - 5x = 0
Next, factor out the common factor (x) from both terms:
x(x^2 - 5) = 0
Now, we have two possibilities for this equation to be true:
1) x = 0
2) x^2 - 5 = 0
For the first possibility, x = 0, we can see that it satisfies the equation x^3 - 5x = 0. However, it is not the largest possible value, as there could be other values of x that satisfy the equation.
For the second possibility, x^2 - 5 = 0, we can solve for x:
x^2 = 5
x = ±√5
Here, we have two possible values for x: √5 (approximately 2.236) and -√5 (approximately -2.236). Both values satisfy the equation x^3 - 5x = 0.
We can conclude that the largest possible value for x that satisfies the equation is √5 (approximately 2.236).