Vì \(a+b=3\)
\(\Rightarrow\left(a+b\right)^2=9\)
\(\Leftrightarrow a^2+b^2+2ab=9\)
\(\Leftrightarrow a^2+b^2=7\)
Vì \(a+b=3\)
\(\Leftrightarrow\left(a+b\right)^3=27\)
\(\Leftrightarrow a^3+b^3+3ab\left(a+b\right)=27\)
\(\Leftrightarrow a^3+b^3=18\)
\(a+b=3\Rightarrow\left(a+b\right)^2=9\)
\(\Rightarrow a^2+2ab+b^2=9\)
\(\Rightarrow a^2-2ab+b^2+4ab=9\)
\(\Rightarrow\left(a-b\right)^2+4=9\)
\(\Rightarrow\left(a-b\right)^2=5\Rightarrow\orbr{\begin{cases}a-b=\sqrt{5}\\a-b=-\sqrt{5}\end{cases}}\)
1)\(a^2+b^2=\left(a+b\right)^2-2ab=9-2=7\)
2)\(a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)=3\left(a^2+b^2-ab\right)=3\cdot7\cdot1=21\)
3)\(a^4+b^4=\left(a^2+b^2\right)^2-2a^2b^2=7^2-2=47\)
4)\(\left(a-b\right)^2=a^2-2ab+b^2\)
\(\Rightarrow\sqrt{\left(a-b\right)^2}=\sqrt{a^2-2ab+b^2}=\sqrt{7-2}=\sqrt{5}\)
\(\Rightarrow a-b=\sqrt{5}\)
5) \(a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)=\sqrt{5}\cdot\left(7+1\right)=8\sqrt{5}\)
