HOC24
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Môn học
Chủ đề / Chương
Bài học
\(\dfrac{3x+2}{\sqrt{x+2}}=2\sqrt{x+2}\\ \Leftrightarrow3x+2=2\left(x+2\right)\\ \Leftrightarrow3x+2=2x+4\\ \Leftrightarrow3x-2x=4-2\\ \Leftrightarrow x=2\)
Vậy......
\(\sqrt{x+4}-\sqrt{1-x}=\sqrt{1-2x}\\ \Leftrightarrow-\sqrt{1-x}=\sqrt{1-2x}-\sqrt{x+4}\\ \Leftrightarrow1-x=1-2x-2\sqrt{\left(1-2x\right)\left(x+4\right)}+x+4\Leftrightarrow-x=-2x-2\sqrt{x+4-2x^2-8x}+x+4\\ \Leftrightarrow-x=-x-2\sqrt{-7x+4-2x^2}+4\\ \Leftrightarrow0=-2\sqrt{-7x+4-2x^2}+4\\ \Leftrightarrow2\sqrt{-7x+4-2x^2}=4\\ \Leftrightarrow\sqrt{-7x+4-2x^2}=2\\ \Leftrightarrow-7x+4-2x^2=4\\ \Leftrightarrow-7x-2x^2=0\\ \Leftrightarrow-x\left(7+2x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}-x=0\\7+2x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x=-\dfrac{7}{2}\left(ktm\right)\end{matrix}\right.\)
\(\dfrac{x-1}{3}-\dfrac{1}{8}=\dfrac{5}{8}\\ \Leftrightarrow8\left(x-1\right)-3=15\\ \Leftrightarrow8x-8-3=15\\ \Leftrightarrow8x-11=15\\ \Leftrightarrow8x=15+11\\ \Leftrightarrow8x=26\\ \Leftrightarrow x=\dfrac{13}{4}\)
Vậy....
\(a)5^{n+1}-4.5^n\\ =\left(5-4\right).5^n\\ =1.5^n\\ =5^n\)
\(b)6^2.6^4-4^3\left(3^6-1\right)\\ =6^6-2^6\left(3^6-1\right)\\ =46656-64\left(3^6-1\right)\\ =46656-64.3^6+64\\ =46720-64.729\\ =46720-46656\\ =64\)
\(x^2-11=0\\ \Leftrightarrow x^2=11\\ \Leftrightarrow\left[{}\begin{matrix}x=11\\x=-\sqrt{11}\end{matrix}\right.\)
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