Răspuns:
Explicație pas cu pas:
[tex](1+\sqrt{x} )(1+\sqrt[4]{x} )(1+\sqrt[8]{x})=\frac{(1+\sqrt{x} )(1+\sqrt[4]{x} )(1+\sqrt[8]{x})(1-\sqrt[8]{x} )}{1-\sqrt[8]{x} } =\frac{(1+\sqrt{x} )(1+\sqrt[4]{x} )(1^{2}-(\sqrt[8]{x} )^{2}}{1-\sqrt[8]{x} } =\frac{(1+\sqrt{x} )(1+\sqrt[4]{x} )(1-\sqrt[4]{x} )}{1-\sqrt[8]{x} } =\frac{(1+\sqrt{x} )(1-\sqrt{x} )}{1-\sqrt[8]{x} } =\frac{1-x}{1-\sqrt[8]{x} }.[/tex]
