Đặt \(A=\sqrt{3+\sqrt{5-2\sqrt{3}}}-\sqrt{3-\sqrt{5-2\sqrt{3}}}\)

\(A^2=3+\sqrt{5-2\sqrt{3}}+3-\sqrt{5-2\sqrt{3}}-2\sqrt{9-5+2\sqrt{3}}\)

\(A^2=6-2\sqrt{4+2\sqrt{3}}=6-2\sqrt{3+2\sqrt{3}+1}=6-2\sqrt{\left(\sqrt{3}+1\right)^2}\)

\(A^2=6-2\left|\sqrt{3}+1\right|=6-2\left(\sqrt{3}+1\right)=6-2\sqrt{3}-2=4-2\sqrt{3}\)

Mà \(\sqrt{3+\sqrt{5-2\sqrt{3}}}>\sqrt{3-\sqrt{5-2\sqrt{3}}}\) nên \(\sqrt{3+\sqrt{5-2\sqrt{3}}}-\sqrt{3-\sqrt{5-2\sqrt{3}}}>0\)

\(\Rightarrow\)\(A=\sqrt{A^2}=\sqrt{4-2\sqrt{3}+1}=\sqrt{3-2\sqrt{3}+1}=\sqrt{\left(\sqrt{3}-1\right)^2}=\sqrt{3}-1\)

... 

\(\sqrt[3]{x+1}=3\)

\(\Rightarrow x+1=3^3=27\)

\(\Rightarrow x=27-1=26\)

\(\sqrt[3]{x=1}=3\)

\(\Rightarrow x+1=3^3=27\)

\(\Rightarrow x=27-1=26\)

a) OB=OC (=R) VÀ AB=AC(/c 2 tt cắt nhau)\(\Rightarrow\)OA LÀ ĐƯỜNG TRUNG TRỤC CỦA BC. b) \(BD\perp AB\)(t/c tt) và BE \(\perp AC\)(A \(\varepsilon\left(O\right)\)đường kính BC ). Aps dụng hệ thúc lượng ta có AE*AC=AB\(^2\)=AC\(^2\).

c) c/m OD\(^2=OB^2=OH\cdot OA\)và OH*OA=OK*OF ( \(\Delta OAK\omega\Delta OFH\left(g-g\right)\))\(\Rightarrow\frac{OD}{OF}=\frac{OK}{OD}\)mà góc FOD chung\(\Rightarrow\Delta OKD\omega\Delta ODF\left(c-g-c\right)\Rightarrow\widehat{ODF}=\widehat{OKD}=90\Rightarrow OD\perp DF\Rightarrowđpcm\)