hi,
i nned to solve this equation:
x^3-5x=8
x=2.7
im unsure how to work this out.
i know i would do 2.7^3-13.5x=8 but i don't know what to do after this.
some help would be great!
thanks!
Let so that you have to find a value of that satisfies the equation . Observe that and . So there lies x , (where ,) such that f(x)=0.
See that . So for to be , you have .
After this take so on and notice when changes its sign. After afew couple of steps you will get the solution according to what precision you want to maintain.
However, the correct solution is
To begin with, think in simple way. and are equivalent. Aren't they? So here solving is equivalent to solving . Alright? You are just subtracting from both the sides; so they must be equivalent.
Next try to understand what does a solution of an equation mean. I suppose you have the preliminary concept regarding function and graph. If you are gievn a function (for example, here you have ), plot in a graph ( that is, put values of along horizontal X-axis and values of along vertical Y-axis). The function will have a solution at if is at (that is ). In this case, your function looks like THIS. The blue line denotes . Notice that as increases, increases ( becomes +ve from -ve). During this increase, the curve cuts the X-axis at some point (red point)-- that particular point is the solution of your equation.
So this is the concept. This is why you should find two consecutive values of such that and , because your required solution always lies in between and
Now I hope you'll understand what my previous post meant.
The red point is the solution: 2.80259