Solve for m

[nycmath]

See attachment.

[Eigenvalue]

m⁶-m³=0

Factor out m³
m³(m³-1)=0

Use the difference of cubes factoring pattern; a³-b³=(a-b)(a²+ab+b²)
m³(m-1)(m²+m+1)=0

Use the quadratic formula to find the solutions for m²+m+1=0
m=[tex]\frac{-1 \pm \sqrt{1²-4(1)(1)} }{2}[/tex]
=[tex]\frac{-1 \pm i\sqrt{3} }{2}[/tex]

m=0, m=1, m=[tex]\frac{-1 \pm i \sqrt{3} }{2}[/tex]

[nycmath]

m⁶-m³=0

Factor out m³
m³(m³-1)=0

Use the difference of cubes factoring pattern; a³-b³=(a-b)(a²+ab+b²)
m³(m-1)(m²+m+1)=0

Use the quadratic formula to find the solutions for m²+m+1=0
m=[tex]\frac{-1 \pm \sqrt{1²-4(1)(1)} }{2}[/tex]
=[tex]\frac{-1 \pm i\sqrt{3} }{2}[/tex]

m=0, m=1, m=[tex]\frac{-1 \pm i \sqrt{3} }{2}[/tex]

I like it! Cool.