\(\sqrt{4+\sqrt{15}}.\)\(\sqrt{4+\sqrt{15}}.\sqrt{4-\sqrt{15}}.\left(\sqrt{10}-\sqrt{6}\right)\)
=\(1.\sqrt{4+\sqrt{15}}.\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\)
=\(\sqrt{8+2\sqrt{15}}.\left(\sqrt{5}-\sqrt{3}\right)=\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)=5-3=2\)
(14,78-a)/(2,87+a)=4/1
14,78+2,87=17,65
Tổng số phần bằng nhau là 4+1=5
Mỗi phần có giá trị bằng 17,65/5=3,53
=>2,87+a=3,53
=>a=0,66.
\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}=2\)
Đặt biểu thức là A, ta có:
\(A=\left(4+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
\(\Leftrightarrow A=\left(4\sqrt{10}-4\sqrt{6}+\sqrt{150}-\sqrt{90}\right)\sqrt{4-\sqrt{15}}\)
\(\Leftrightarrow A=\left(4\sqrt{10}-4\sqrt{6}+\sqrt{25}\sqrt{6}-\sqrt{9}\sqrt{10}\right)\sqrt{4-\sqrt{15}}\)
\(\Leftrightarrow A=\left(4\sqrt{10}-4\sqrt{6}+5\sqrt{6}-3\sqrt{10}\right)\sqrt{4-\sqrt{15}}\)
\(\Leftrightarrow A=\left(\sqrt{10}+\sqrt{6}\right)\sqrt{4+\sqrt{15}}\)
\(\Leftrightarrow A=\sqrt{\left(\sqrt{10}+\sqrt{6}\right)^2\left(4-\sqrt{15}\right)}\)
\(\Leftrightarrow A=\sqrt{\left(16+2\sqrt{60}\right)\left(4-\sqrt{15}\right)}\)
\(\Leftrightarrow A=\sqrt{64-16\sqrt{15}+8\sqrt{60}-2\sqrt{900}}\)
\(\Leftrightarrow A=\sqrt{64-16\sqrt{15}+8\sqrt{4}\sqrt{15}-2.30}\)
\(\Leftrightarrow A=\sqrt{64-60-16\sqrt{15}+16\sqrt{15}}\)
\(\Leftrightarrow A=\sqrt{4}\)
\(\Leftrightarrow A=2\)
=> Biểu thức = 2