a) 25x2 – 100 = 106 c) (x – 3) (x + 7) = 0 d) (x + 2) (x – 4) = -5 Giai giúp em

Đáp án:

\(\begin{array}{l}
a)\left[ \begin{array}{l}
x = \dfrac{{\sqrt {206} }}{5}\\
x =  - \dfrac{{\sqrt {206} }}{5}
\end{array} \right.\\
c)\left[ \begin{array}{l}
x = 3\\
x =  - 7
\end{array} \right.\\
d)\left[ \begin{array}{l}
x =  - 1\\
x = 3
\end{array} \right.
\end{array}\)

Giải thích các bước giải:

\(\begin{array}{l}
a)25{x^2} - 100 = 106\\
 \to 25{x^2} = 206\\
 \to {x^2} = \dfrac{{206}}{{25}}\\
 \to \left| x \right| = \dfrac{{\sqrt {206} }}{5}\\
 \to \left[ \begin{array}{l}
x = \dfrac{{\sqrt {206} }}{5}\\
x =  - \dfrac{{\sqrt {206} }}{5}
\end{array} \right.\\
c)\left( {x - 3} \right)\left( {x + 7} \right) = 0\\
 \to \left[ \begin{array}{l}
x - 3 = 0\\
x + 7 = 0
\end{array} \right.\\
 \to \left[ \begin{array}{l}
x = 3\\
x =  - 7
\end{array} \right.\\
d)\left( {x + 2} \right)\left( {x - 4} \right) =  - 5\\
 \to {x^2} - 2x - 8 + 5 = 0\\
 \to {x^2} - 2x - 3 = 0\\
 \to {x^2} + x - 3x - 3 = 0\\
 \to x\left( {x + 1} \right) - 3\left( {x + 1} \right) = 0\\
 \to \left( {x + 1} \right)\left( {x - 3} \right) = 0\\
 \to \left[ \begin{array}{l}
x =  - 1\\
x = 3
\end{array} \right.
\end{array}\)