Đáp án:
Giải thích các bước giải:
Đặt $A=\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}$
$\sqrt{2}A=\sqrt{2}.\sqrt{4-\sqrt{7}}-\sqrt{2}.\sqrt{4+\sqrt{7}}$
$\sqrt{2}A=\sqrt{8-2\sqrt{7}}-\sqrt{8+2\sqrt{7}}$
$\sqrt{2}A=\sqrt{7-2.\sqrt{7}.1+1}-\sqrt{7+2.\sqrt{7}.1+1}$
$\sqrt{2}A=\sqrt{(\sqrt{7}-1)^2}-\sqrt{(\sqrt{7}+1)^2}$
$\sqrt{2}A=|\sqrt{7}-1|-|\sqrt{7}+1|$
$\sqrt{2}A=\sqrt{7}-1-\sqrt{7}-1$
$\sqrt{2}A=-2$
$⇒A=\dfrac{-2}{\sqrt{2}}$
$⇒A=-\sqrt{2}$
Vậy $A=-\sqrt{2}$.