Question

Rút gọn biểu thức sau : A = \(\sqrt{3+2\sqrt{ }2}\) - \(\sqrt{3-2\sqrt{ }2}\)

B = \(\dfrac{1}{\sqrt{3}-1_{ }}-\dfrac{1}{\sqrt{3}+1}\)

Mọi người giúp mình với ạ !!! cảm ơn nhiều ạ !!! :)

Answer 1

\(A=\sqrt{2+2\sqrt{2}+1}-\sqrt{2-2\sqrt{2}+1}\)
\(A=\sqrt{\left(\sqrt{2}+1\right)^2}-\sqrt{\left(\sqrt{2}-1\right)^2}\)
\(A=\sqrt{2}+1-\left|\sqrt{2}-1\right|\)
\(A=\sqrt{2}+1-\left(\sqrt{2}-1\right)\) ( vì căn 2 > 1)
\(A=2\)

Answer 2

\(B=\dfrac{\sqrt{3}+1-\left(\sqrt{3}-1\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)}\)
\(B=\dfrac{2}{3-1}=\dfrac{2}{2}=1\)