So, my dear friend. Wtf you're doing? Your solution is very wrong. First: what if you check -2 as solution. Oops it is. So you missed some of the solution. In fact this strange thing has 18 complex solution. You lost some when you drasticly make a qubic root as a first step, then you lost half of the solution when you not spot, the normal root can gives you more solution. So i think technically all complex solutions are: 2*(1 on power 1/18 on power 0,1,2, ...,17). From this the real solutions are 2 and -2.
Your solution is too complicated. Now in the modern age, solving math problems is simple and concise, easy to understand. There are many people who know how to solve math problems, so why complicate the problem? In my opinion, first take the square root of x to the power of 6, then raise it to the power of three, then the left side is still x to the power of 9, the right side decomposes 512 into 2 to the power of nine, so the problem is solved (method Expose the function, if the powers are the same then the bases are the same)
It’s in my head.
(Sqrt[x^6])^3=512 x=2 x=-1 ±Sqrt[3]i
(X^6/2)^3= x^3.3=×^27=512/ x=
X=2
So, my dear friend. Wtf you're doing? Your solution is very wrong. First: what if you check -2 as solution. Oops it is. So you missed some of the solution. In fact this strange thing has 18 complex solution. You lost some when you drasticly make a qubic root as a first step, then you lost half of the solution when you not spot, the normal root can gives you more solution. So i think technically all complex solutions are: 2*(1 on power 1/18 on power 0,1,2, ...,17). From this the real solutions are 2 and -2.
Your solution is too complicated. Now in the modern age, solving math problems is simple and concise, easy to understand. There are many people who know how to solve math problems, so why complicate the problem?
In my opinion, first take the square root of x to the power of 6, then raise it to the power of three, then the left side is still x to the power of 9, the right side decomposes 512 into 2 to the power of nine, so the problem is solved (method Expose the function, if the powers are the same then the bases are the same)
Зачем эти лишние манипуляции??
для особо тупых