Đáp án:
a. \(\left[ \begin{array}{l}
x = 10\\
x = - 5
\end{array} \right.\)
Giải thích các bước giải:
\(\begin{array}{l}
a.{\left( {x - 2} \right)^2} + 2\left( {x - 2} \right)\left( {x - 3} \right) + {\left( {x - 3} \right)^2} = {15^2}\\
\to {x^2} - 4x + 4 + 2\left( {{x^2} - 5x + 6} \right) + {x^2} - 6x + 9 = 225\\
\to 4{x^2} - 20x - 200 = 0\\
\to {x^2} - 5x - 50 = 0\\
Xét: Δ= 25 + 4.50 = 225 > 0\\
\to \left[ \begin{array}{l}
x = 10\\
x = - 5
\end{array} \right.\\
b.DK:x \ge - 12\\
25{\left( {x + 1} \right)^2} - 10\left( {x + 1} \right)\left( {x - 3} \right) + {\left( {x - 3} \right)^2} = {\left( {x + 12} \right)^2}\\
\to 25\left( {{x^2} + 2x + 1} \right) - 10\left( {{x^2} - 2x - 3} \right) + {x^2} - 6x + 9 = {x^2} + 24x + 144\\
\to 15{x^2} + 40x - 80 = 0\\
Xét: Δ= {40^2} + 4.15.80 = 6400 > 0\\
\to \left[ \begin{array}{l}
x = \frac{4}{3}\\
x = - 4
\end{array} \right.
\end{array}\)
