Question

[Bùi Hạnh Nguyên]

Câu 1:

a)\(\left|\frac{1}{3}x-8\right|+3=15\)

b)\(15-\left|2+3x\right|=8\)

c)\(\left|1\frac{1}{3}x-5\right|=4=18\)

d)\(-1\frac{1}{6}-\left|5-3x\right|=\frac{2}{3}\)

e)\(\left(\frac{3}{7}\right)^{20}:\left(\frac{9}{49}\right)^6\)

g)\(4.2^5:\left(2^3.1^{16}\right)\)

Có ai onl trả lời giúp với :(

Answer 1

[Nobi Nobita]

a) \(\left|\frac{1}{3}x-8\right|+3=15\)

\(\Leftrightarrow\left|\frac{1}{3}x-8\right|=12\)

\(\Leftrightarrow\orbr{\begin{cases}\frac{1}{3}x-8=-12\\\frac{1}{3}x-8=12\end{cases}}\Leftrightarrow\orbr{\begin{cases}\frac{1}{3}x=-4\\\frac{1}{3}x=20\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-12\\x=60\end{cases}}\)

Vậy \(x\in\left\{-12;60\right\}\)

b) \(15-\left|2+3x\right|=8\)

\(\Leftrightarrow\left|2+3x\right|=7\)

\(\Leftrightarrow\orbr{\begin{cases}2+3x=-7\\2+3x=7\end{cases}}\Leftrightarrow\orbr{\begin{cases}3x=-9\\3x=5\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-3\\x=\frac{5}{3}\end{cases}}\)

Vậy \(x\in\left\{-3;\frac{5}{3}\right\}\)

d) \(-1\frac{1}{6}-\left|5-3x\right|=\frac{2}{3}\)

\(\Leftrightarrow\frac{-7}{6}-\left|5-3x\right|=\frac{2}{3}\)

\(\Leftrightarrow\left|5-3x\right|=\frac{-7}{6}-\frac{2}{3}\)

\(\Leftrightarrow\left|5-3x\right|=\frac{-11}{6}\)

Vì \(\left|5-3x\right|\ge0\forall x\)

mà \(\frac{-11}{6}< 0\)\(\Rightarrow\)Vô lý 

Vậy \(x\in\varnothing\)

Answer 2

[Nobi Nobita]

e) \(\left(\frac{3}{7}\right)^{20}:\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{20}:\left[\left(\frac{3}{7}\right)^2\right]^6=\left(\frac{3}{7}\right)^{20}:\left(\frac{3}{7}\right)^{2.6}\)

\(=\left(\frac{3}{7}\right)^{20}:\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^8\)

g) \(4.2^5:\left(2^3.1^{16}\right)=2^2.2^5:2^3=2^4=16\)