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Given that x2+x+1=0x^2+x+1=0x2+x+1=0, find the value of (x+1x)2+(x2+1x2)2+⋯+(x6+1x6)2(x+\dfrac{1}{x})^2+(x^2+\dfrac{1}{x^2})^2+\dots +(x^6+\dfrac{1}{x^6})^2(x+x1)2+(x2+x21)2+⋯+(x6+x61)2.
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