5x^4=5x
Can you please help
5x^4=5x
x^4 - x = 0
x(x^3 - 1) = 0
x = 0 or x^3 = 1
x = 0 or x = 1
There are also two complex roots, but I don't think you have studied that.
Let me know if you did.
Yes I have but how to you find them
the above factor of x^3 - 1 factors to
(x-1)(x^2 + x + 1)
the x-1 = 0 gave us x = 1
x^2 + x + 1 = 0
x = (-1 ±√-3)/2
or
x = (-1 ± i√3)/2
Thank you
Of course! To solve this equation, we want to find the value(s) of x that make the equation true. Let's go through the steps:
Step 1: First, we can simplify the equation by dividing both sides by 5, since it is a common factor on both sides:
5x^4 / 5 = 5x / 5
This simplifies to:
x^4 = x
Step 2: Next, we notice that both sides of the equation have x to some power. We can try to simplify it further by subtracting x from both sides to set the equation equal to zero:
x^4 - x = 0
Step 3: Now, we have a fourth-degree polynomial equation. To solve it, we can try factoring if possible, or find the roots using numerical methods or a graphing calculator.
In this case, factoring may not be simple. One option is to use a numerical method, such as the Newton-Raphson method or the bisection method, to find the approximate values of x that satisfy the equation.
Another option is to use a graphing calculator or software to graph the equation y = x^4 - x, and find the x-coordinate(s) of the point(s) where the graph intersects the x-axis (where y=0).
These methods will give you the approximate values of x that make the equation true.
I hope this helps! Let me know if you have any further questions.