=10+2căn 21-10+2căn 21
=4*căn 21
Lời giải:
$(\sqrt{7}+\sqrt{3})^2-(\sqrt{7}-\sqrt{3})^2$
$=7+3+2\sqrt{21}-(7+3-2\sqrt{21})$
$=4\sqrt{21}$
\(\left(\sqrt{7}+\sqrt{3}\right)^2-\left(\sqrt{7}-\sqrt{3}\right)^2\)
\(=\left[\left(\sqrt{7}+\sqrt{3}\right)-\left(\sqrt{7}+\sqrt{3}\right)\right].\left[\left(\sqrt{7}+\sqrt{3}\right)+\left(\sqrt{7}-\sqrt{3}\right)\right]\)
\(=\left(\sqrt{7}+\sqrt{3}-\sqrt{7}+\sqrt{3}\right).\left(\sqrt{7}+\sqrt{3}+\sqrt{7}-\sqrt{3}\right)\)
\(=2\sqrt{3}.2\sqrt{7}\)
\(=4\sqrt{21}\)
\(Hoặc\)
\(=\left(7+2.\sqrt{7}.\sqrt{3}+3\right)-\left(7-2.\sqrt{7}.\sqrt{3}+3\right)\)
\(=7+2\sqrt{21}+3-7+2\sqrt{21}-3\)
\(=4\sqrt{21}\)
