solve x^6=5x-x^3?

Question

what are the steps to solving it??????

Answer 1

x^6 + x^3 - 5x = 0
x(x^5 + x^2 - 5)=0
x=0 or x^5 + x^2 - 5 = 0
you need to find 5 more roots that make equation = 0
for a total of 6 roots

Answer 2

you mean x^6 + 5x + 8 = 0 ? you can try to get an approximate solution using any method like newton raphson method etc you need to start with an intial guess and iterate it should be obvious looking at this polynomial it is increasing ast both negative and positive x and has a minumum when the derivative 5x^5 + 5 = 0 or x = -1 so 1 - 5 +8 = 4 is the lowest value of this polynomial equation so it will never quiet make it to zero what exactly did you want to solve again ? please give us the complete question. all the best

Answer 3

either x=sqrt 5
or
x=cuberootof 4
i guess