1. Tính giá trị các biểu thức
a) \(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)
b) \(\left(\dfrac{1}{\sqrt{5}-\sqrt{2}}-\dfrac{1}{\sqrt{5}+\sqrt{2}}+1\right)\cdot\dfrac{1}{\left(\sqrt{2}+1\right)^2}\)
2. Cho biểu thức : C = \(\sqrt{4+4\sqrt{x-4}}+\sqrt{x-4\sqrt{x-4}}\) ( với x >= 4 )
a) rút gọn
b) tính giá trị của C khi x = \(\sqrt{15+\sqrt{6}}\)
1) a) \(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-1\right)^2}\)
\(=\left|\sqrt{3}+1\right|-\left|\sqrt{3}-1\right|=\sqrt{3}+1-\left(\sqrt{3}-1\right)=\sqrt{3}+1-\sqrt{3}+1=2\)
b) \(\left(\dfrac{1}{\sqrt{5}-\sqrt{2}}-\dfrac{1}{\sqrt{5}+\sqrt{2}}+1\right).\dfrac{1}{\left(\sqrt{2}+1\right)^2}\)
\(=\left(\dfrac{\sqrt{5}+\sqrt{2}-\left(\sqrt{5}-\sqrt{2}\right)}{\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{5}+\sqrt{2}\right)}+1\right).\dfrac{1}{\left(\sqrt{2}+1\right)^2}\)
\(=\left(\dfrac{\sqrt{5}+\sqrt{2}-\sqrt{5}+\sqrt{2}}{\left(\sqrt{5}\right)^2-\left(\sqrt{2}\right)^2}+1\right).\dfrac{1}{\left(\sqrt{2}+1\right)^2}\)
\(=\left(\dfrac{2\sqrt{2}}{5-2}+1\right).\dfrac{1}{\left(\sqrt{2}+1\right)^2}=\left(\dfrac{2\sqrt{2}}{3}+1\right).\dfrac{1}{\left(\sqrt{2}+1\right)^2}\)
\(=\dfrac{3+2\sqrt{2}}{3}.\dfrac{1}{\left(\sqrt{2}+1\right)}=\dfrac{\left(\sqrt{2}+1\right)^2}{3}.\dfrac{1}{\left(\sqrt{2}+1\right)}=\dfrac{1}{3}\)
Bạn Nguyen Van Tuan ơi giải hộ mk baì này tí.
