Question

[rin sốt cà]

giúp tớ vs các cậu ơiiiii

Answer 1

[Nguyễn Lê Phước Thịnh]

1:

1: \(2\sqrt{12}+3\sqrt{18}-3\sqrt{75}-\sqrt{50}\)

\(=4\sqrt{3}-15\sqrt{3}+9\sqrt{2}-5\sqrt{2}\)

\(=-11\sqrt{3}+4\sqrt{2}\)

2: \(\sqrt{16-6\sqrt{7}}+\sqrt{\left(3+\sqrt{7}\right)^2}\)

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

\(=\left|3-\sqrt{7}\right|+\left|3+\sqrt{7}\right|\)

\(=3-\sqrt{7}+3+\sqrt{7}=6\)

3:

\(\dfrac{6}{\sqrt{7}-1}+\dfrac{4}{\sqrt{7}-3}+\dfrac{7}{\sqrt{7}}\)

\(=\dfrac{6\left(\sqrt{7}+1\right)}{7-1}-\dfrac{4}{3-\sqrt{7}}+\sqrt{7}\)

\(=\sqrt{7}+1+\sqrt{7}-\dfrac{4\left(3+\sqrt{7}\right)}{2}\)

\(=2\sqrt{7}+1-2\left(3+\sqrt{7}\right)\)

=1-6

=-5

2:

a: ĐKXĐ: x>=5

\(5\sqrt{x-5}+\sqrt{4x-20}-\sqrt{9x-45}=12\)

=>\(5\sqrt{x-5}+2\sqrt{x-5}-3\sqrt{x-5}=12\)

=>\(4\sqrt{x-5}=12\)

=>\(\sqrt{x-5}=3\)

=>x-5=9

=>x=14(nhận)

2:

ĐKXĐ: \(x\in R\)

\(\sqrt{4x^2-20x+25}=1\)

=>\(4x^2-20x+25=1\)

=>(2x-5)²=1

=>\(\left[{}\begin{matrix}2x-5=1\\2x-5=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=6\\2x=4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=2\end{matrix}\right.\)