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If the roots of p(x)=x3+3x2+4x−8p(x) = x^3 + 3x^2 + 4x - 8p(x)=x3+3x2+4x−8 are a\color{#D61F06}{a}a, b\color{#3D99F6}{b}b and c\color{#69047E}{c}c, what is the value of
a2(1+a2)+b2(1+b2)+c2(1+c2)?\color{#D61F06}{a}^2 \big(1 + \color{#D61F06}{a}^2\big) + \color{#3D99F6}{b}^2 \big(1 + \color{#3D99F6}{b}^2\big) + \color{#69047E}{c}^2 \big(1 + \color{#69047E}{c}^2\big)?a2(1+a2)+b2(1+b2)+c2(1+c2)?
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