Question

plz solve it in full process
$n {}^{3} - 3n {}^{2} - 2n = 9240$
find the value of n in process

Answer 1

Factorising the equation is the way to go, however this one is very tedious.
${ n}^{3} - 3 {n}^{2} - 2n - 9240 = 0$
For equations concerning the third power of a variable, we use a trial and error method to find one of the roots.

We can see that when we take n=22 we get a value of 9152 which is less than 9240 and when we take n=23 we get 10534 which is more than 9240 so we can be sure that one root of the equation is between 22 and 23.

On closer inspection we find that the root is 22.06655586882885 approximately.

On looking at the signs of the coefficients and some basic calculations we also find that the other two roots of the cubic equation are imaginary and thus require a lot of calculation to find, which I am not gonna write, but I will give you the other two roots.

-9.533277934414425 + i* 18.106623984896178

and

-9.533277934414425 - i* 18.106623984896178

However since ether question states find THE value of n, it refers to it's real value which we found earlier. Hence the answer is

22.06655586882885