Question

10.cho biểu thức:p=\(\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right).\left(\dfrac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)\)

a) rút gọn p

b)tìm a để p \(< 7-4\sqrt{3}\)

Answer 1

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

\(=\left(\sqrt{a}+1\right)^2\left(\sqrt{a}-1\right)^2=\left(a-1\right)^2\)

b) đk: a khác 1

\(P< 7-4\sqrt{3}\Leftrightarrow\left(a-1\right)^2< 7-4\sqrt{3}\Leftrightarrow a-1< \sqrt{7-4\sqrt{3}}\)

\(\Leftrightarrow a-1< \sqrt{\left(4-2\cdot2\cdot\sqrt{3}+3\right)}\Leftrightarrow a-1< 2-\sqrt{3}\Leftrightarrow a< 2-\sqrt{3}+1\)

\(\Leftrightarrow a< 3-\sqrt{3}\)

Kl:..

Answer 2

kl nhớ thêm đk a khác 1