对数计算例题03-变式

\begin{array}{c}
解:(\lg{2})^3+(\lg{5})^3+3\lg{2} \cdot \lg{5}\\
设:\lg{2}=a,\lg{5}=b\\
得:a^3+b^3+3ab\\
\because (a+b)(a^2-ab+b^2) \Rightarrow a^3+b^3\\
\therefore a^3+b^3+3ab \Rightarrow (a+b)(a^2-ab+b^2)+3ab\\
\\
已知:\lg{2}+\lg{5}=\lg{(2\cdot5)}=1\\
\therefore a^2-ab+b^2+3ab
\\
a^2+2ab+b^2
\\(a+b)^2
\\ result = 1
\end{array}

标签：03,ab,变式,lg,3ab,therefore,array,例题,Rightarrow
来源： https://www.cnblogs.com/Preparing/p/16098107.html