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Algebra Level 3

If the roots of x 2 + x + 1 = 0 x^2 + x + 1 = 0 are D D and E E , what is the value of ( 1 − D ) ( 1 − E ) (1-D)(1-E) ?

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Aman Joshi by Aman Joshi , 18, India

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1 solution

Rishu Jaar
Nov 4, 2017

Here, x 2 + x + 1 = ( x − D ) ( x − E ) (since D and E are the roots) \large x^2+x+1=(x-D)(x-E) \hspace{1cm} \color{#3D99F6}{ \text{(since D and E are the roots)}} Plug in x = 1 → x=1 \rightarrow

⟹ ( 1 − D ) ( 1 − E ) = 1 + 1 + 1 = 3 \large\implies (1-D)(1-E)=1+1+1= \color{#69047E}{\boxed{3}}

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