Question

Solve:
64x^6-65x^3=-1

Answer 1

solve
\[64z^2-65z+1=0\] the replace z by \(x^3\)

Answer 2

get
\[(64z-1)(z+1)=0\]
\[z=-1,z=\frac{1}{64}\] then solve
\[x^3=-1,x^3=\frac{1}{64}\]

Answer 3

ok that should give me 6 answers correct

Answer 4

i think satellite has made a little mistake.
\[64z^2-65z+1=0\]
after that it should be
\[(64z-1)(z-1)=0\]
then
\[x^3=1, \frac{1}{64}\]
I think there are only 2 answers which are 1 and 1/4.

P.s. if there are mistakes, please tell me.

Answer 5

but the original problem is x^6