Question

Answer 1

a: ĐKXĐ: x>=0; x<>1

b: \(f\left(4-2\sqrt{3}\right)=f\left(\left(\sqrt{3}-1\right)^2\right)=\dfrac{\sqrt{3}-1+1}{\sqrt{3}-1-1}\)

\(=\dfrac{\sqrt{3}}{\sqrt{3}-2}=-3-2\sqrt{3}\)

\(f\left(a^2\right)=\dfrac{\left|a\right|+1}{\left|a\right|-1}=\dfrac{-a+1}{-a-1}=\dfrac{a-1}{a+1}\)

c: f(x)=căn 3

=>\(\dfrac{\sqrt{x}+1}{\sqrt{x}-1}=\sqrt{3}\)

=>\(\sqrt{x}+1=\sqrt{3}\cdot\sqrt{x}-\sqrt{3}\)

=>\(\sqrt{x}\left(1-\sqrt{3}\right)=-\sqrt{3}-1\)

=>\(\sqrt{x}=\dfrac{-\sqrt{3}-1}{-\sqrt{3}+1}=\dfrac{\sqrt{3}+1}{\sqrt{3}-1}=2+\sqrt{3}\)

=>\(x=\left(2+\sqrt{3}\right)^2=7+4\sqrt{3}\)