Question

Answer 1

1: Đặt \(x=\sqrt[3]{2};y=\sqrt[3]{5}\)

=>\(x^3=2;y^3=5\)

=>\(x^4=2x;y^4=5y\)

\(\sqrt[3]{20}=\sqrt[3]{4\cdot5}=x^2y;\sqrt[3]{25}=y^2\)

\(\left(\sqrt[3]{2}+\sqrt[3]{20}-\sqrt[3]{25}\right)^2=\left(x+x^2y-y^2\right)^2\)

\(=x^2+x^4y^2+y^4+2x^3-2x^2y^3-2xy^2\)

\(=x^2+2x\cdot y^2+5y+2\cdot2y-2x^2\cdot5-2xy^2=x^2+5y+4y-10x^2\)

\(=9\left(y-x^2\right)=9\cdot\left(\sqrt[3]{5}-\sqrt[3]{4}\right)\)

=>\(\left(\sqrt[3]{2}+\sqrt[3]{20}-\sqrt[3]{25}\right)^2=9\left(\sqrt[3]{5}-\sqrt[3]{4}\right)\)

=>\(\left(\sqrt[3]{2}+\sqrt[3]{20}-\sqrt[3]{25}\right)^{}=3\cdot\sqrt{\left(\sqrt[3]{5}-\sqrt[3]{4}\right)}\)