Tìm x, biết: (a) 2x^2−6x=0. (b) (x+1)^2=3(x+1).

a) \(2{x^2} - 6x = 0\)

\(2x\left( {x - 3} \right) = 0\)

Suy ra \(x = 0\) hoặc \(x - 3 = 0\)

\(x = 0\) hoặc \(x = 3\)

Vậy \(x \in \left\{ {0;3} \right\}.\)

b) \({\left( {x + 1} \right)^2} = 3\left( {x + 1} \right)\)

\({\left( {x + 1} \right)^2} - 3\left( {x + 1} \right) = 0\)

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

Suy ra \(x + 1 = 0\) hoặc \(x - 2 = 0\)

\(x = - 1\) hoặc \(x = 2\)

Vậy \(x \in \left\{ { - 1;2} \right\}.\)

c) \({\left( {x - 1} \right)^3} - \left( {x + 3} \right)\left( {{x^2} - 3x + 9} \right) + 3{x^2} = 11\)

\({x^3} - 3{x^2} + 3x - 1 - \left( {{x^3} + {3^3}} \right) + 3{x^2} = 11\)

\({x^3} - 3{x^2} + 3x - 1 - {x^3} - 27 + 3{x^2} = 11\)

\(3x = 39\)

\(x = 13\)

Vậy \(x = 13.\)