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#2
19 ธันวาคม 2014, 10:31
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$x^3-x^2-x-1=0$
ให้ $x=y+\frac{1}{3}$ $\Big(y+\frac{1}{3}\Big)^3-\Big(y+\frac{1}{3}\Big)^2-\Big(y+\frac{1}{3}\Big)-1=0$ $y^3-\frac{4}{3}y-\frac{38}{27}=0$ ให้ $y=u+v$ $u^3+v^3+3uv(u+v)-\frac{4}{3}(u+v)-\frac{38}{27}=0$ $u^3+v^3+(u+v)(3uv-\frac{4}{3})-\frac{38}{27}=0$ $uv=\frac{4}{9}$ ,$u=\frac{4}{9v}$ แทนค่ากลับ $\frac{4^3}{(9v)^3}+v^3-\frac{38}{27}=0$ $v=\frac{1}{3}\sqrt[3]{19-3\sqrt{33}}$ ,$u=\frac{1}{3}\sqrt[3]{19+3\sqrt{33}}$ $y=u+v$ $y=\frac{1}{3}\sqrt[3]{19-3\sqrt{33}}+\frac{1}{3}\sqrt[3]{19+3\sqrt{33}}$ $x=\frac{1}{3}+\frac{1}{3}\sqrt[3]{19-3\sqrt{33}}+\frac{1}{3}\sqrt[3]{19+3\sqrt{33}}$
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Hope is what makes us strong. It's why we are here. It is what we fight with when all else is lost. 
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#3
19 ธันวาคม 2014, 10:38
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เชิงซ้อนอีก 2 ตัวรบกวนท่านอื่นช่วยหาด้วยนะครับ
__________________
Hope is what makes us strong. It's why we are here. It is what we fight with when all else is lost.
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