Question

Answer 1

\(a,4x^2-17x=0\)

\(x\left(4x-17\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{17}{4}\end{matrix}\right.\)

\(b,3x^2-2=0\)

\(x^2=\dfrac{2}{3}\)

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

\(c,x^2-5x+4=0\)

\(x^2-x-4x+4=0\)

\(\left(x-1\right)\left(x-4\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=1\\x=4\end{matrix}\right.\)

\(d,3\left(x-2\right)^2=2\left(x^2-4\right)\)

\(\left(x-2\right)\left(3x-6\right)-\left(x-2\right)\left(2x+4\right)=0\)

\(\left(x-2\right)\left(x-10\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x=10\end{matrix}\right.\)

Answer 2

a: =>x(4x-17)=0

=>x=0 hoặc x=17/4

b: =>3x²=2

=>x²=2/3

hay \(x\in\left\{\dfrac{\sqrt{6}}{3};-\dfrac{\sqrt{6}}{3}\right\}\)

c: =>(x-1)(x-4)=0

=>x=1 hoặc x=4

d: \(\Leftrightarrow\left(x-2\right)\left(3x-6\right)-\left(x-2\right)\left(2x+4\right)=0\)

=>(x-2)(x-10)=0

=>x=2 hoặc x=10

Answer 3

Answer 4

a)\(4x^2-17x=0\)

\(\Leftrightarrow x.\left(4x-17\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\4x-17=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{17}{4}\end{matrix}\right.\)

Vậy ...

b)\(3x^2-2=0\)

\(\Leftrightarrow3x^2=2\)

\(\Leftrightarrow x^2=\dfrac{2}{3}\)

\(\Leftrightarrow x=\pm\sqrt{\dfrac{2}{3}}\)

Vậy....

c)\(x^2-5x+4=0\)

\(\Leftrightarrow x^2-x-4x+4=0\)

\(\Leftrightarrow x.\left(x-1\right)-4.\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-4\right).\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=1\end{matrix}\right.\)

Vậy....

d)\(3.\left(x-2\right)^2=2.\left(x^2-4\right)\)

\(\Leftrightarrow3.\left(x-2\right)^2-2.\left(x^2-4\right)=0\)

\(\Leftrightarrow3.\left(x-2\right).\left(x-2\right)-2.\left(x+2\right).\left(x-2\right)=0\)

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

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

\(\Leftrightarrow\left[{}\begin{matrix}3x-6-2x-4=0\\x=2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-10=0\\x=2\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=10\\x=2\end{matrix}\right.\)

Vậy...