[2+5w+2w2}6={2+2w+5w2}6=729 prove that - Maths - Complex Numbers and Quadratic Equations

Question

[2+5w+2w2}6={2+2w+5w2}6=729
prove that

Santosh Kumar · Accepted Answer

${(2 + 5 w + 2 w^{2})}^{6} = {(1 + w + w^{2}) + (1 + w + w^{2}) + 3 w}^{6} = (3 w)^{6} = 729 w^{6} = 729 (w^{3})^{2} = 729$

${(2 + 2 w + 5 w^{2})}^{6} = {(1 + w + w^{2}) + (1 + w + w^{2}) + (3 w^{2})}^{6} = (3 w^{2})^{6} = 729 w^{12} = 729 (w^{3})^{4} = 729 ∴ {(2 + 5 w + 2 w^{2})}^{6} = {(2 + 2 w + 5 w^{2})}^{6} = 729$