Question

a) Tính giá trị của các biểu thức:

1) \(\sqrt{120}-\left(\sqrt{5}+\sqrt{6}\right)^2\)

2) \(5\sqrt{18}-\sqrt{50}+\sqrt{8}\)

b) Tìm x, biết: \(\sqrt{x+1}-\sqrt{4x+4}+\sqrt{9x+9}=1\)

Answer 1

1. \(\sqrt{120}-\left(\sqrt{5}+\sqrt{6}\right)^2\\ =\sqrt{4.30}-\left(5+2.\sqrt{5.6}+6\right)\\ =2\sqrt{30}-11-2\sqrt{30}\\ =-11\)

2. \(5\sqrt{18}-\sqrt{50}+\sqrt{8}\\ =5\sqrt{9.2}-\sqrt{25.2}+\sqrt{4.2}\\ =15\sqrt{2}-5\sqrt{2}+2\sqrt{2}\\ =12\sqrt{2}\)

3. \(\sqrt{x+1}-\sqrt{4x+4}+\sqrt{9x+9}=1\\ \Leftrightarrow\sqrt{x+1}-\sqrt{4\left(x+1\right)}+\sqrt{9\left(x+1\right)}=1\\ \Leftrightarrow\sqrt{x+1}-2\sqrt{x+1}+3\sqrt{x+1}=1\\ \Leftrightarrow2\sqrt{x+1}=1\\ \Leftrightarrow\sqrt{x+1}=\dfrac{1}{2}\\ \Leftrightarrow x+1=\dfrac{1}{4}\\ \Leftrightarrow x=-\dfrac{3}{4}\)