\(\sqrt[3]{26+15\sqrt{3}}-\sqrt[3]{26-15\sqrt{3}}\)
\(=\sqrt[3]{\left(\sqrt{3}+2\right)^3}-\sqrt[3]{\left(\sqrt{3}-2\right)^3}\)
\(=\sqrt{3}+2-\sqrt{3}+2\)
`=4`
\(B^3=26+15\sqrt{3}-26+15\sqrt{3}-3\cdot\sqrt[3]{1}\cdot B\)
\(\Leftrightarrow B^3+3B-30\sqrt{3}=0\)
\(\Leftrightarrow B=2\sqrt{3}\)
x+x2+x3=x(1+x+x2)=x[(x2+2x+1)−x]x+x2+x3=x(1+x+x2)=x[(x2+2x+1)−x]
=x[(x+1)2−(√x)2]=x(x+1−√x)(x+1+√x)