Question

\(P=\dfrac{a-\sqrt{a}}{a-1}\)

a, Rút gọn P

b, Tính giá trị của P khi a = \(8-2\sqrt{7}\)

MÌNH ĐAG CẦN ĐÁP ÁN GẤP!!!

CẢM ƠN CÁC BẠN <3

Answer 1

ĐK:a\(\ge0,a\ne1\)

a) \(P=\dfrac{a-\sqrt{a}}{a-1}=\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\left(\sqrt{a}-1\right)\left(\sqrt{a}+1\right)}=\dfrac{\sqrt{a}}{\sqrt{a}+1}\)

b) Khi a=\(8-2\sqrt{7}\) thì P=\(\dfrac{\sqrt{8-2\sqrt{7}}}{\sqrt{8-2\sqrt{7}}+1}=\dfrac{\sqrt{7-2\sqrt{7}+1}}{\sqrt{7-2\sqrt{7}+1}+1}=\dfrac{\sqrt{\left(\sqrt{7}-1\right)^2}}{\sqrt{\left(\sqrt{7}-1\right)^2}+1}=\dfrac{\left|\sqrt{7}-1\right|}{\left|\sqrt{7}-1\right|+1}=\dfrac{\sqrt{7}-1}{\sqrt{7}}=\dfrac{\sqrt{7}\left(\sqrt{7}-1\right)}{7}=\dfrac{7-\sqrt{7}}{7}\)