(*ZnO材料Cij;*)k = (20.97 - 10.51^2/21.09)*10^10*(1 + I*100^-1)
(*PET材料;*)l = (0.38 - (0.22^2/0.43))*10^10*(1 + I*100^-1)
(*Al材料;*)m = (11.1 - (6.1^2/11.1))*10^10*(1 + I*100^-1)
(*ZnO密度*)n = 5.606*10^3
(*PET密度*)o = 1.4*10^3
(*Al密度*)p = 2.7*10^3
a = 30*10^-9*l + 40*10^-9*m + 200*10^-9*k
b = ((30^2*10^-9*10^-9/2)*l) + ((((70*10^-9)^2 - (30*10^-9)^2)/2)*
m) + ((((270*10^-9)^2 - (70*10^-9)^2)/2)*k)
c = b
d = (((30*10^-9)^3/3)*l) + ((((70*10^-9)^3 - (30*10^-9)^3)/3)*
m) + ((((270*10^-9)^3 - (70*10^-9)^3)/3)*k)
e = 30*o + 40*p + 200*n
f = (((30*10^-9)^2/2)*o) + ((((70*10^-9)^2 - (30*10^-9)^2)/2)*
p) + ((((270*10^-9)^2 - (70*10^-9)^2)/2)*n)
g = f
h = (((30*10^-9)^3/3)*o) + ((((70*10^-9)^3 - (30*10^-9)^3)/3)*
p) + ((((270*10^-9)^3 - (70*10^-9)^3)/3)*n)
A = {{a*i^2 + e*j^2,
c*i^2 + g*j^2}, {(b*i^4 + f*j^2*i^2), (d*i^4 + h*j^2*i^2 - e*j^2)}}
A // MatrixForm
Det[A]
Solve[Det[A] == 0, i]

看不懂就多看会儿

含有一个未知数的六次方程能解出靠谱的答案吗？
------------------------------
能啊，下面这个就可以
eq = 2*x^6 + 3*y^6 == 0
Solve[eq, x]