Question

[Minh Hằng Vũ]

 

Answer 1

[Nguyễn Lê Phước Thịnh]

Bài 2:

1: \(\dfrac{1}{5^{x-1}}+3\cdot5^{2-x}=\dfrac{16}{125}\)

=>\(\dfrac{1}{5^x\cdot\dfrac{1}{5}}+3\cdot\dfrac{25}{5^x}=\dfrac{16}{125}\)

=>\(\dfrac{5}{5^x}+\dfrac{75}{5^x}=\dfrac{16}{125}\)

=>\(\dfrac{80}{5^x}=\dfrac{16}{125}\)

=>\(5^x=80\cdot\dfrac{125}{16}=5\cdot125=5^4\)

=>x=4

2: \(\left(3-\left|x-\dfrac{1}{2}\right|\right)\left(\dfrac{8}{15}-\dfrac{1}{5}\right)+\dfrac{2}{3}=1\)

=>\(\left(3-\left|x-\dfrac{1}{2}\right|\right)\cdot\dfrac{1}{3}=1-\dfrac{2}{3}=\dfrac{1}{3}\)

=>\(3-\left|x-\dfrac{1}{2}\right|=1\)

=>\(\left|x-\dfrac{1}{2}\right|=3-1=2\)

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

Bài 3:

1: Gọi ba phần được chia lần lượt là x,y,z

Ba phần tỉ lệ với 2/5;3/4;1/6 nên \(\dfrac{x}{\dfrac{2}{5}}=\dfrac{y}{\dfrac{3}{4}}=\dfrac{z}{\dfrac{1}{6}}\)

=>\(2,5x=\dfrac{4}{3}y=6z\)

=>\(15x=8y=36z\)

=>\(\dfrac{15x}{360}=\dfrac{8y}{360}=\dfrac{36z}{360}\)

=>\(\dfrac{x}{24}=\dfrac{y}{45}=\dfrac{z}{10}=k\)

=>x=24k; y=45k; z=10k

\(x^2+y^2+z^2=24309\)

=>\(\left(24k\right)^2+\left(45k\right)^2+\left(10k\right)^2=24309\)

=>\(k^2=9\)

=>\(\left[{}\begin{matrix}k=3\\k=-3\end{matrix}\right.\)

TH1: k=3

=>\(x=24\cdot3=72;y=45\cdot3=135;z=10\cdot3=30\)

TH2: k=-3

=>\(x=24\cdot\left(-3\right)=-72;y=45\cdot\left(-3\right)=-135;z=10\cdot\left(-3\right)=-30\)