Câu 10:

Chứng minh:

a) \((\sqrt{3}-1)^{2}=4-2 \sqrt{3}\)

b) \(\sqrt{4-2 \sqrt{3}}-\sqrt{3}=-1\)

Lời giải:

a) Ta có: VT = \((\sqrt{3}-1)^{2}=(\sqrt{3})^{2}-2 \sqrt{3}+1\)

= \(3-2 \sqrt{3}+1=4-2 \sqrt{3}\) = VP

Vậy \((\sqrt{3}-1)^{2}=4-2 \sqrt{3}\) (đpcm)

b) Theo câu a) ta có:

VT = \(\sqrt{4-2 \sqrt{3}}-\sqrt{3}=\sqrt{(\sqrt{3}-1)^{2}}-\sqrt{3}\)

= \(|\sqrt{3}-1|-\sqrt{3}=\sqrt{3}-1-\sqrt{3}\)

= -1 = VP (vì \(\sqrt{3} -1\) > 0) (đpcm)