Tìm x, biết (a) x(3x−5)+7x−3x^2=10. (b) (x−2)(x+2)+(2x+1)^2+1=5x^2−3x.
Giải thích
a) \[x\left( {3x - 5} \right) + 7x - 3{x^2} = 10\]
\[\begin{array}{l}3{x^2} - 5x + 7x - 3{x^2} = 10\\2x = 10\\x = 5\end{array}\]
b) \[\left( {x - 2} \right)\left( {x + 2} \right) + {\left( {2x + 1} \right)^2} + 1 = 5{x^2} - 3x\]
\[\begin{array}{l}{x^2} - 4 + 4{x^2} + 4x + 1 + 1 = 5{x^2} - 3x\\7x = 2\\x = \frac{2}{7}\end{array}\]
c) \[{\left( {x + 1} \right)^3} - \left( {3x + 1} \right)\left( {2x - 2} \right) = {x^3} + 7x - 9\]
\[\begin{array}{l}{x^3} + 3{x^2} + 3x + 1 - 6{x^2} + 6x - 2x + 2 = {x^3} + 7x - 9\\ - 3{x^2} + 12 = 0\\ - 3\left( {{x^2} - 4} \right) = 0\\{x^2} - 4 = 0\\{x^2} = 4\end{array}\]
\[x = 2\] hoặc \[x = - 2\]
Vậy \[x \in \left\{ { - 2;2} \right\}\]