Đáp án:
Giải thích các bước giải:
Ta có:
$VT.\sqrt{2}=\sqrt{12+4\sqrt{3}+4\sqrt{5}+2\sqrt{15}}-\sqrt{8+2\sqrt{15}}$
$=\sqrt{4+3+5+2.2.\sqrt{3}+2.2.\sqrt{5}+2.\sqrt{3}.\sqrt{5}}-\sqrt{3+2.\sqrt{3}.\sqrt{5}+5}$
$=\sqrt{(2+\sqrt{3}+\sqrt{5})^2}-\sqrt{(\sqrt{3}+\sqrt{5})^2}$
$=|2+\sqrt{3}+\sqrt{5}|-|\sqrt{3}+\sqrt{5}|$
$=(2+\sqrt{3}+\sqrt{5})-(\sqrt{3}+\sqrt{5})$
$=2+\sqrt{3}+\sqrt{5}-\sqrt{3}-\sqrt{5}$
$=2$
$⇒VT=\sqrt{2}=VP$ (đpcm)