第7題
\(\begin{align}
  & f\left( x \right)={{b}_{1}}\left( x-{{a}_{2}} \right)\left( x-{{a}_{3}} \right)+{{b}_{2}}\left( x-{{a}_{3}} \right)\left( x-{{a}_{1}} \right)+{{b}_{3}}\left( x-{{a}_{1}} \right)\left( x-{{a}_{2}} \right)-\left( x-{{a}_{1}} \right)\left( x-{{a}_{2}} \right)\left( x-{{a}_{3}} \right) \\
& f\left( {{a}_{1}} \right)>0,f\left( {{a}_{2}} \right)<0,f\left( {{a}_{3}} \right)>0,f\left( \infty  \right)<0 \\
\end{align}\)

第 3 題
用柯西或參數式搭配疊合與和角也可以

第8題
\(\begin{align}
  & \log {}_{a}10+\log {}_{b}10+\log {}_{c}10=\log {}_{abc}10 \\
& \frac{1}{\log a}+\frac{1}{\log b}+\frac{1}{\log c}=\frac{1}{\log \left( abc \right)} \\
& \log a=x,\log b=y,\log c=z \\
& \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{1}{x+y+z} \\
& \frac{yz+zx+xy}{xyz}=\frac{1}{x+y+z} \\
& xyz+{{y}^{2}}z+y{{z}^{2}}+z{{x}^{2}}+xyz+{{z}^{2}}x+{{x}^{2}}y+x{{y}^{2}}+xyz=xyz \\
& {{x}^{2}}y+x{{y}^{2}}+{{y}^{2}}z+y{{z}^{2}}+{{z}^{2}}x+z{{x}^{2}}+2xyz=0 \\
& \left( x+y \right)\left( y+z \right)\left( z+x \right)=0 \\
& ab=1\ or\ bc=1\ or\ ca=1 \\
& {{(abc)}^{4}}-{{(abc)}^{2}}({{a}^{2}}+{{b}^{2}}+{{c}^{2}})+{{a}^{2}}{{b}^{2}}+{{b}^{2}}{{c}^{2}}+{{c}^{2}}{{a}^{2}}=1 \\
\end{align}\)