2. จาก $x^2+x+1=0$ และ $x\not=0$ จะได้ว่า
$x+1+\frac{1}{x}=0$
$x+\frac{1}{x}=-1$------------->$(x+\frac{1}{x})^2=1$
$x^2+\frac{1}{x^2}=(x+\frac{1}{x})^2-2=-1$--------->$(x^2+\frac{1}{x^2})^2=1$
$x^3+\frac{1}{x^3}=(x+\frac{1}{x})(x^2+\frac{1}{x^2})-(x+\frac{1}{x})=2$---------->$(x^3+\frac{1}{x^3})^2=4$
$x^4+\frac{1}{x^4}=(x^2+\frac{1}{x^2})^2-2=-1$--------->$(x^4+\frac{1}{x^4})^2=1$
$x^5+\frac{1}{x^5}=(x^2+\frac{1}{x^2})(x^3+\frac{1}{x^3})-(x+\frac{1}{x})=-1$------>$(x^5+\frac{1}{x^5})^2=1$
$x^6+\frac{1}{x^6}=(x^3+\frac{1}{x^3})^2-2=2$------>$(x^6+\frac{1}{x^6})^2=4$
ดังนั้น ผลบวก $=(1+1+4)+(1+1+4)+....+(1+1+4)$ $9$วงเล็บ
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