Question

c)3x^2-7x-10=0

d)2x(x-10)-x+10=0

e)3x^3+7x^2+17x+5=0

f)(2x-1)^2-(x-3)^2=0

g)x^3-5x^2+8x=4

 

Answer 1

tìm x nha

 

Answer 2

c, \(3x^2-7x+10=0\)

\(\Leftrightarrow3x^2+3x-10x+10=0\)

\(\Leftrightarrow3x\left(x+1\right)-10\left(x+1\right)=0\)

\(\Leftrightarrow\left(x+1\right)\left(3x-10\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\dfrac{10}{3}\end{matrix}\right.\)

Answer 3

d, \(2x\left(x-10\right)-x+10=0\)

\(\Leftrightarrow2x\left(x-10\right)-\left(x-10\right)=0\)

\(\Leftrightarrow\left(x-10\right)\left(2x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=10\\x=\dfrac{1}{2}\end{matrix}\right.\)

Answer 4

e, \(3x^3+7x^2+17x+5=0\)

\(\Leftrightarrow3x^3+x^2+6x^2+2x+15x+5=0\)

\(\Leftrightarrow3x^2\left(3x+1\right)+2x\left(3x+1\right)+5\left(3x+1\right)=0\)

\(\Leftrightarrow\left(3x+1\right)\left(3x^2+2x+5\right)=0\)

\(\Leftrightarrow3x+1=0\)

\(\Leftrightarrow x=-\dfrac{1}{3}\)

Answer 5

f, \(\left(2x-1\right)^2-\left(x-3\right)^2=0\)

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

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

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

Answer 6

g, \(x^3-5x^2+8x=4\)

\(\Leftrightarrow x^3-x^2-4x^2+4x+4x-4=0\)

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

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

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)^2=0\)

 

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

Answer 7

c. \(3x^2-7x-10=0\)

\(\Leftrightarrow\left(x-\dfrac{10}{3}\right)\left(x+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{10}{3}=0\\x+1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{10}{3}\\x=-1\end{matrix}\right.\)

b. \(2x\left(x-10\right)-x+10=0\)

\(\Leftrightarrow2x\left(x-10\right)-\left(x-10\right)=0\)

\(\Leftrightarrow\left(x-10\right)\left(2x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-10=0\\2x-1=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=10\\x=\dfrac{1}{2}\end{matrix}\right.\)

c. \(3x^3+7x^2+17x+5=0\)

\(\Leftrightarrow x^2\left(3x+1\right)+2x\left(3x+1\right)+5\left(3x+1\right)=0\)

\(\Leftrightarrow\left(3x+1\right)\left(x^2+2x+5\right)=0\)

mà \(x^2+2x+5=\left(x+1\right)^2+4\ge4>0\forall x\)

\(\Leftrightarrow3x+1=0\)

\(\Leftrightarrow x=-\dfrac{1}{3}\)

f. \(\left(2x-1\right)^2-\left(x-3\right)^2=0\)

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

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

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

g. \(x^3-5x^2+8x=4\)

\(\Leftrightarrow x^3-5x^2+8x-4=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)^2=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-2=0\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

Answer 8

f. (2x - 1)² - (x - 3)² = 0

<=> (2x - 1 - x + 3)(2x - 1 + x - 3) = 0

<=> (x + 2)(3x - 4) = 0

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