解答
x16−1=0
解答
x=1,x=−1,x=i,x=−i,x=21+21i,x=−21−21i,x=−21+21i,x=21−21i,x=2432−11+4232−1i,x=−2432−11−4232−1i,x=−2431+21+4231+2i,x=2431+21−4231+2i,x=2431+21+4231+2i,x=−2431+21−4231+2i,x=−2432−11+4232−1i,x=2432−11−4232−1i
求解步骤
x16−1=0
将 1到右边
x16=1
用u=x2 和 u8=x16改写方程式u8=1
解 u8=1:u=1,u=−1,u=i,u=−i,u=21+21i,u=−21−21i,u=−21+21i,u=21−21i
u=1,u=−1,u=i,u=−i,u=21+21i,u=−21−21i,u=−21+21i,u=21−21i
代回 u=x2，求解 x
解 x2=1:x=1,x=−1
解 x2=−1:x=i,x=−i
解 x2=i:x=21+21i,x=−21−21i
解 x2=−i:x=−21+21i,x=21−21i
解 x2=21+21i:x=2432−11+4232−1i,x=−2432−11−4232−1i
解 x2=−21−21i:x=−2431+21+4231+2i,x=2431+21−4231+2i
解 x2=−21+21i:x=2431+21+4231+2i,x=−2431+21−4231+2i
解 x2=21−21i:x=−2432−11+4232−1i,x=2432−11−4232−1i
解为
x=1,x=−1,x=i,x=−i,x=21+21i,x=−21−21i,x=−21+21i,x=21−21i,x=2432−11+4232−1i,x=−2432−11−4232−1i,x=−2431+21+4231+2i,x=2431+21−4231+2i,x=2431+21+4231+2i,x=−2431+21−4231+2i,x=−2432−11+4232−1i,x=2432−11−4232−1i