Question

1) Tính

a) \(\sqrt{14+6\sqrt{5}}-\sqrt{\dfrac{\sqrt{5}-2}{\sqrt{5}+2}}\)

b) \(\dfrac{2\left(\sqrt{2}-\sqrt{6}\right)}{3\sqrt{2}-\sqrt{3}}\)

2) giải phương trình

\(\sqrt{4x+8}+\sqrt{9x+18}-\sqrt{9}=\sqrt{16x+32}\)

Answer 1

1.

\(\sqrt{14+6\sqrt{5}}-\sqrt{\dfrac{\sqrt{5}-2}{\sqrt{5}+2}}\)

=\(\sqrt{9+6\sqrt{5}+5}-\dfrac{\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+2}}\)

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

= \(3+\sqrt{5}-\dfrac{\sqrt{5-4}}{\sqrt{\left(\sqrt{5}+2\right)^2}}\)

= \(\dfrac{3\left(\sqrt{5}+2\right)}{\sqrt{5+2}}+\dfrac{\sqrt{5}\left(\sqrt{5}+2\right)}{\sqrt{5}+2}-\dfrac{1}{\sqrt{5}+2}\)

=\(\dfrac{5\sqrt{5}+10}{\sqrt{5}+2}=\dfrac{5\left(\sqrt{5}+2\right)}{\sqrt{5}+2}=5\)

Answer 2

2, \(\sqrt{4x+8}+\sqrt{9x+18}-\sqrt{9}=\sqrt{16x+32}\)
⇔\(\sqrt{4\left(x+2\right)}+\sqrt{9\left(x+2\right)}-3=\sqrt{16\left(x+2\right)}\)
⇔\(2\sqrt{x+2}+3\sqrt{x+2}-4\sqrt{x+2}=3\)
\(\Leftrightarrow\sqrt{x+2}=3\)
⇔\(x+2=9\)
⇔x=7