Question

Rút gọn biểu thức sau:

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

Answer 1

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

ĐKXD: a=1 a<0

a=1 => A=0

a,=>A=\(\sqrt{1-a}\)+\(\sqrt{a\left(a-1\right)}\)+a\(\sqrt{\frac{a-1}{a}}\)

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

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

       =\(\sqrt{1-a}\)

Answer 2

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