星座生肖性格解读:代数化简

解答：
（2+5^0.5）*（2-5^0.5）=-1
所以设T1=(2+5^0.5)^(1/3)
T2=(2-5^0.5)^(1/3)
那么
T1*T2=-1
(T1)^3+(T2)^3=4
有设T0=(2+5^0.5)^(1/3)+(2-5^0.5)^(1/3)
=T1+T2
以下来求T0，
（T0）^3=(T1+T2)^3=(T1)^3+(T2)^3+3*(TI+T2)*T1*T2
=4+3*(T0)*(-1)
即得到
（TO）^3+3*T0-4=0
因式分解得到：
（TO-1）*（T0^2+T0+4)=0
得到唯一解
T0=1
所以
(2+5^0.5)^(1/3)+(2-5^0.5)^(1/3)=1

观察2+5^0.5与2-5^0.5恰为负倒数，设前者为x后者即为-1/x
我们来计算一下[x^(1/3)+(-1/x）^(1/3)]^3
=[x^(1/3)-(1/x）^(1/3)]^3
=[x^(1/3)-x^(-1/3)]^3
=x-x^[(2/3)-(1/3)]+x^[(1/3)-(2/3)]-x
=3[x^(-1/3)-x^(1/3)]
令x^(1/3)-x^(-1/3）=t
则方程就是t^3=3t
因为t不等于0，并且t大于0。于是，t=3^0.5
得解

观察2+5^0.5与2-5^0.5恰为负倒数，设前者为x后者即为-1/x
我们来计算一下[x^(1/3)+(-1/x）^(1/3)]^3
=[x^(1/3)-(1/x）^(1/3)]^3
=[x^(1/3)-x^(-1/3)]^3
=x-x^[(2/3)-(1/3)]+x^[(1/3)-(2/3)]-1/x
=3[x^(-1/3)-x^(1/3)]+x-1/x
=3[x^(-1/3)-x^(1/3)]+4
令x^(1/3)-x^(-1/3）=t
则方程就是t^3=4-3t
因式分解得(t-1)(t^2+t+4)=0
得到t=1