a) \(2x\left(x-3\right)+3\left(x-3\right)=0\)

\(\Leftrightarrow\left(x-3\right)\left(2x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-3=0\\2x+3=0\end{matrix}\right.\)

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

b) \(x\left(3x-1\right)-5\left(1-3x\right)=0\)

\(\Leftrightarrow x\left(3x-1\right)+5\left(3x-1\right)=0\)

\(\Leftrightarrow\left(3x-1\right)\left(x+5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-1=0\\x+5=0\end{matrix}\right.\)

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

a)
\(=\sqrt{10\left(x+2\right)}=\sqrt{10}.\sqrt{x+2}\)
\(\sqrt{x+2}\ge0=>x+2\ge0=>x\ge-2\)
b)
\(=\dfrac{\sqrt{99}}{\sqrt{4x-1}}\)
\(=>4x-1>0=>4x>1=>x>\dfrac{1}{4}\)
c)
\(=\dfrac{\sqrt{-5x-10}}{\sqrt{2021}}=>-5x-10\ge0\)
\(=>-5\left(x+2\right)\ge0\)
\(=>x+2\ge0=>x\ge-2\)

a: ĐKXĐ: \(x\ge-2\)

b: ĐKXĐ: \(x>\dfrac{1}{4}\)

c: ĐKXĐ: \(x\le-2\)

\(a,5^x+5^{x+2}=650\\ \Rightarrow a,5^x+5^x.25=650\\ \Rightarrow26.5^x=650\\ \Rightarrow5^x=25\\ \Rightarrow5^x=5^2\\ \Rightarrow x=2\)

\(b,3^{x.1}+5.3^{x.1}=162\\ \Rightarrow3^x+5.3^x=162\\ \Rightarrow6.3^x=162\\ \Rightarrow3^x=27\\ \Rightarrow3^x=3^3\\ \Rightarrow x=3\)

a: \(\Leftrightarrow5^x=25\)

hay x=2

a, <=> 5^x + 5^x .5² =650

<=> 5^x +25.5^x =650

<=> 26.5^x =650

<=> 5^x =25

<=> 5^x = 5²

<=> x=2

b, <=> 6. 3^x =162

 <=> 3^x =27

<=> 3^x =3³

<=> x=3

Chúc bạn học tốt nha!

a) Ta có: \(\left(2x+1\right)^2-\left(3x-4\right)^2=0\)

\(\Leftrightarrow\left(2x+1-3x+4\right)\left(2x+1+3x-4\right)=0\)

\(\Leftrightarrow\left(5-x\right)\left(5x-3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=5\\x=\dfrac{3}{5}\end{matrix}\right.\)

b) Ta có: \(5x^3-3x^2+10x-6=0\)

\(\Leftrightarrow x^2\left(5x-3\right)+2\left(5x-3\right)=0\)

\(\Leftrightarrow5x-3=0\)

hay \(x=\dfrac{3}{5}\)

a) \(\Rightarrow72-20x-36x+84=30x-240-6x-84\)

\(\Rightarrow80x=480\Rightarrow x=6\)

b) \(\Rightarrow15x+25-8x+12=5x+6x+36+1\)

\(\Rightarrow4x=0\Rightarrow x=0\)

c) \(\Rightarrow10x-16-12x+15=12x-16+11\)

\(\Rightarrow14x=4\Rightarrow x=\dfrac{2}{7}\)

\(a,\Leftrightarrow\left(x^2-8x+16\right)-10=0\\ \Leftrightarrow\left(x-4\right)^2-10=0\\ \Leftrightarrow\left(x-4-\sqrt{10}\right)\left(x-4+\sqrt{10}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=4+\sqrt{10}\\x=4-\sqrt{10}\end{matrix}\right.\\ b,\Leftrightarrow10\left(2x-1\right)+6x=9x\\ \Leftrightarrow20x-10-3x=0\\ \Leftrightarrow17x=10\Leftrightarrow x=\dfrac{10}{17}\)

E = 3( x² - 5x/4 + 25/4) -25/4 +1

GTNN E = -21/4