Question

proved that (2+5w+2w²)⁶=729​

Answer 1

Answer:

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Question:-

Prove that

${(2 + 5w + {2w}^{2}) }^{6} = 726$

Formula used :-

Complex cube roots of unity

$\large\bold\red{◇ \: 1 + w + {w}^{2} = 0}$

$\large\bold\red{◇ \: {w}^{3} = 1 }$

Solution:-

${(2 + 5w + {2w}^{2}) }^{6}$

$⟹ \: {(5w + 2(1 + {w}^{2})) }^{6}$

$= {(5w - 2w)}^{6}$

$= {(3w)}^{6}$

$= {3}^{6} \times {w}^{6}$

$= 729 \times 1$

$= 729$

$\large\bold\red{hence, \: proved}$

$\huge \fcolorbox{black}{cyan}{◇Hope it helps U◇}$