Question

Tìm x, biết

a) x\(^2\) - 10x = -25

b) x. (x + 2) - 3. (x + 2) = 0

c) (2x - 1). (x - 5) - 2x\(^2\) + 10x - 25 = 0

d) x\(^3\) - 4x\(^2\) - x + 4 = 0

e) x\(^3\) - 6x\(^2\) + 12x - 8 = 27

Answer 1

a.

`x^2-10x=-25`

\(\Leftrightarrow x^2-10x+25=0\)

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

\(\Leftrightarrow x-5=0\)

\(\Leftrightarrow x=5\)

b.

`x(x+2)-3(x+2)=0`

`\Leftrightarrow (x+2)(x-3)=0`

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

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

Answer 2

c.

`(2x-1)(x-5)-2x^2+10x-25=0`

`Leftrightarrow 2x^2 -11x +5-2x^2 +10x-25=0`

`Leftrightarrow -x-20 =0`

`Leftrightarrow x=-20`

d.

`x^3 -4x^2 -x+4=0`

`Leftrightarrow x^2 (x-4) -(x-4)=0`

`Leftrightarrow (x-4)(x^2-1)=0`

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x^2-1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\pm1\end{matrix}\right.\)

Answer 3

e.

`x^3 -6x^2+12x -8 =27`

`Leftrightarrow (x-2)^3 =3^3`

`Leftrightarrow x-2=3`

`Leftrightarrow x=5`