Question

[Ender MC]

Tính

\(\sqrt{15x^2-8x\sqrt{15}+16}\) tại x=\(\sqrt{15}\)

Rút gọn

\(\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}\) - \(\dfrac{6+2\sqrt{6}}{\sqrt{3}+\sqrt{2}}\)

help :(

Answer 1

[tran nguyen bao quan]

Tại x=15\(\Rightarrow\sqrt{15x^2-8x+\sqrt{15}+16}=\sqrt{15.\left(\sqrt{15}\right)^2-8.\sqrt{15}.\sqrt{15}+16}=\sqrt{15^2-2.15.4+4^2}=\sqrt{\left(15-4\right)^2}=\sqrt{11^2}=11\)

Ta có \(\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}-\dfrac{6+2\sqrt{6}}{\sqrt{3}+\sqrt{2}}=\dfrac{\sqrt{3}\left(\sqrt{5}-2\right)}{\sqrt{5}-2}+\dfrac{2\sqrt{3}\left(\sqrt{3}+\sqrt{2}\right)}{\sqrt{3}+\sqrt{2}}=\sqrt{3}+2\sqrt{3}=3\sqrt{3}\)