Đáp án: $A=2$
Giải thích các bước giải:
$A=(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}})^2$
$⇒2A=2(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}})^2$
$=(\sqrt{8+2\sqrt{7}}-\sqrt{8-2\sqrt{7}})^2$
$=(\sqrt{7+2\sqrt{7}+1}-\sqrt{7-2\sqrt{7}+1})^2$
$=[\sqrt{(\sqrt{7}+1)^2}-\sqrt{(\sqrt{7}-1)^2}]^2$
$=(|\sqrt{7}+1|-|\sqrt{7}-1|)^2$
$=[(\sqrt{7}+1)-(\sqrt{7}-1)]^2$
$=(\sqrt{7}+1-\sqrt{7}+1)^2$
$=2^2=4$
$⇒A=4÷2=2$
