Question

[Đỗ Lê Kiên]

giúp mình với

Answer 1

[Member lỗi thời :>>]

\(\left(\frac{3}{4}\right)^x=\frac{81}{28^8}\)

\(\Rightarrow\left(\frac{3}{4}\right)^x=\frac{3^4}{\left(4.7\right)^8}\)

\(\Rightarrow\left(\frac{3}{4}\right)^x=\frac{3^4}{4^8.7^8}\)

\(\Rightarrow\left(\frac{3}{4}\right)^x=\frac{3^4}{4^4.4^4}:7^8\)

\(\Rightarrow\left(\frac{3}{4}\right)^x=\frac{3^4}{4^4}:\left(7^2\right)^4:4^4\)

\(\Rightarrow\frac{3^4}{4^4}:\left(\frac{3}{4}\right)^x=49^4.4^4\)

\(\Rightarrow\left(\frac{3}{4}\right)^4:\left(\frac{3}{4}\right)^x=\left(49.4\right)^4\)

\(\Rightarrow\left(\frac{3}{4}\right)^{4-x}=196^4\)

\(\Rightarrow\left(\frac{3}{4}\right)^{4-x}=196^{4-x}.196^4\)

\(\Rightarrow196^{4-x}:\left(\frac{3}{4}\right)^{4-x}=196^4\)

\(\Rightarrow\left(196:\frac{3}{4}\right)^{4-x}=196^4:\left(\frac{3}{4}\right)^4.\left(\frac{3}{4}\right)^4\)

\(\Rightarrow\left(196:\frac{3}{4}\right)^{4-x}=\left(196:\frac{3}{4}\right)^4.\left(\frac{3}{4}\right)^4\)

\(\Rightarrow\left(196:\frac{3}{4}\right)^{4-x}:\left(196:\frac{3}{4}\right)^4=\left(\frac{3}{4}\right)^4\)

\(\Rightarrow\left(\frac{196:\frac{3}{4}}{196:\frac{3}{4}}\right)^{4-x-4}=\left(\frac{3}{4}\right)^4\)

\(\Rightarrow1^{-x}=\left(\frac{3}{4}\right)^4\)=> Vô lý

Answer 2

[Member lỗi thời :>>]

| x - 1 | + | x² - 1 | = 0

Vì \(\hept{\begin{cases}\left|x-1\right|\ge0,\forall x\\\left|x^2-1\right|\ge0,\forall x\end{cases}}\)=> | x - 1 | + | x² - 1 | ≥ 0 ∀ x

Dấu " = " xảy ra <=> \(\hept{\begin{cases}\left|x-1\right|=0\\\left|x^2-1\right|=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x-1=0\\x^2-1=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=1\\x^2=1\end{cases}}\Leftrightarrow\hept{\begin{cases}x=1\\x=\pm1\end{cases}}\Leftrightarrow x=1\)