Question

Rút gọn biểu thức

\(\sqrt{\left(7+4\sqrt{3}\right)\left(a-1\right)^2}\)

A= \(\sqrt{a+2\sqrt{a-1}}+\sqrt{a-2\sqrt{a-1}}\) với 1<x<2

Answer 1

a, =\(\sqrt{\left[\left(\sqrt{3}\right)^2+2.\sqrt{3}.2+2^2\right]\left(a-1\right)^2}\)

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

=\(\left(\sqrt{3}+2\right)\left|a-1\right|\)

Answer 2

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

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

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

+Với a<2 thì a-1<1 => \(\sqrt{a-1}< 1\)

khi đó A=\(\left(\sqrt{a-1}+1\right)-\left(\sqrt{a-1}-1\right)\)= 2

Answer 3

Nhớ chọn mình nha!!!!