Question

Giúp mk với:
Tính:

\(D=\sqrt{12-3\sqrt{7}}-\sqrt{12+3\sqrt{7}}\)

Answer 1

\(D^2=24-2\sqrt{144-9.7}=24-2\sqrt{144-63}=24-2\sqrt{81}=6\)

Answer 2

mà:D<0\(\Rightarrow D=-\sqrt{6}\)

Answer 3

Nhận xét : \(D< 0\)

Bình phương ta có :

\(D^2=12-3\sqrt{7}+12+3\sqrt{7}-2\sqrt{\left(12-3\sqrt{7}\right)\left(12+3\sqrt{7}\right)}\)

\(=24-2\sqrt{81}=24-2.9=6\)

\(\Rightarrow\orbr{\begin{cases}D=\sqrt{6}\\D=-\sqrt{6}\end{cases}}\) Mà \(D< 0\)

Nên \(D=-\sqrt{6}\)