Question

CHỨNG MINH :

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

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

Answer 1

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

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

VT=\(3-2\sqrt{3}.1+1\)

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

=> VT=VP

vậy .........

Answer 2

a) VT = \(\left(\sqrt{3}-1\right)^2\) = \(\left(\sqrt{3}\right)^2-2\sqrt{3}+1^2\) = \(3-2\sqrt{3}+1=4-2\sqrt{3}\) = VP

vậy \(\left(\sqrt{3}-1\right)^2=4-2\sqrt{3}\) (đpcm)

b) VT = \(\sqrt{4-2\sqrt{3}}-\sqrt{3}\) = \(\sqrt{\left(\sqrt{3}\right)^2-2\sqrt{3}.1+1^2}-\sqrt{3}\)

= \(\sqrt{\left(\sqrt{3}-1\right)^2}-\sqrt{3}\) = \(\left|\sqrt{3}-1\right|-\sqrt{3}\) = \(\sqrt{3}-1-\sqrt{3}=-1\) = VP

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

Answer 3

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

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

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

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

VT= -1

=> VT=VT

vậy...................