Question

Rút gọn \(A=\frac{\sqrt{\sqrt[4]{8}+\sqrt{\sqrt{2}-1}}-\sqrt{\sqrt[4]{8}-\sqrt{\sqrt{2}-1}}}{\sqrt{\sqrt[4]{8}-\sqrt{\sqrt{2}+1}}}\)

Answer 1

A>0

Bình phương A được :

\(A^2=\frac{\sqrt[4]{8}+\sqrt{\sqrt{2}-1}-2\sqrt{\left(\sqrt[4]{8}+\sqrt{\sqrt{2}-1}\right)\left(\sqrt[4]{8}-\sqrt{\sqrt{2}-1}\right)}+\sqrt[4]{8}-\sqrt{\sqrt{2}-1}}{\sqrt[4]{8}-\sqrt{\sqrt{2}+1}}\)

=\(\frac{2\sqrt[4]{8}-2\sqrt{\sqrt{8}-\sqrt{2}+1}}{\sqrt[4]{8}-\sqrt{\sqrt{2}+1}}\)=\(\frac{2\sqrt[4]{8}-2\sqrt{2\sqrt{2}-\sqrt{2}+1}}{\sqrt[4]{8}-\sqrt{\sqrt{2}+1}}=\frac{2\sqrt[4]{8}-2\sqrt{\sqrt{2}+1}}{\sqrt[4]{8}-\sqrt{\sqrt{2}+1}}=2\)

=> A= \(\sqrt{2}\)

Answer 2

@Vũ Minh Tuấn @Lê Thị Thục Hiền @No choice teen