Question

câu 1 : tính

a,\(\sqrt{\left(\sqrt{5}-3\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\)

b,\(\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}\)

c,\(\sqrt{3}x^2-\sqrt{12}=0\)

ba câu đó e đag thắc mắc mà chưa giải được m.n có lòng tốt giúp e vs ạ mai ktra r huhu.

Answer 1

a ) \(\sqrt{\left(\sqrt{5}-3\right)^2}+\sqrt{\left(\sqrt{5}-2\right)^2}\)

\(=\left|\sqrt{5}-3\right|+\left|\sqrt{5}-2\right|\)

\(=3-\sqrt{5}+\sqrt{5}-2\)

\(=1\)

b ) \(\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}\)

\(=\sqrt{5+2\sqrt{15}+3}-\sqrt{5-2\sqrt{15}+3}\)

\(=\sqrt{\left(\sqrt{5}+\sqrt{3}\right)^2}-\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}\)

\(=\left|\sqrt{5}+\sqrt{3}\right|-\left|\sqrt{5}-\sqrt{3}\right|\)

\(=2\sqrt{3}\)

c ) \(\sqrt{3}x^2-\sqrt{12}=0\)

\(\Leftrightarrow\sqrt{3}x^2=\sqrt{12}\)

\(\Leftrightarrow x^2=\sqrt{\dfrac{12}{3}}=2\)

\(\Leftrightarrow x=\sqrt{2}\)