Question

Chứng minh

\(\left(4+\sqrt{15}\right)\left(10-\sqrt{16}\right)\sqrt{4-\sqrt{15}}=2\)

Answer 1

(Đề của you hình như sai!)

\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}=2\)

Xét vế trái, ta có:

\(VT=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)

\(\Leftrightarrow\left(4\sqrt{10}-4\sqrt{6}+5\sqrt{6}-3\sqrt{10}\right).\left(\sqrt{\frac{5}{2}}-\sqrt{\frac{3}{2}}\right)\)

\(\Leftrightarrow\left(\sqrt{10}+\sqrt{6}\right).\left(\sqrt{\frac{5}{2}}-\sqrt{\frac{3}{2}}\right)\)

\(\Leftrightarrow5-\sqrt{15}+\sqrt{15}-3=2=VP\left(đpcm\right)\)

(Nhớ k cho mình với nhá!)