Đáp án:
$\begin{array}{l}
3)d)\left( {3x - 5} \right)\left( {7 - 5x} \right) - \left( {5x + 2} \right)\left( {2 - 3x} \right) = 4\\
\Leftrightarrow 21x - 15{x^2} - 35 + 25x\\
- 10x + 15{x^2} - 4 + 6x = 4\\
\Leftrightarrow 42x = 43\\
\Leftrightarrow x = \dfrac{{43}}{{42}}\\
Vậy\,x = \dfrac{{43}}{{42}}\\
e){\left( {x + 2} \right)^2} + {\left( {x - 3} \right)^2} - 2\left( {x - 1} \right)\left( {x + 1} \right) = 9\\
\Leftrightarrow {x^2} + 4x + 4 + {x^2} - 6x + 9\\
- 2\left( {{x^2} - 1} \right) = 9\\
\Leftrightarrow 2{x^2} - 2x + 13 - 2{x^2} + 2 = 9\\
\Leftrightarrow 2x = 6\\
\Leftrightarrow x = 3\\
Vậy\,x = 3\\
f){\left( {4x + 3} \right)^2} - {\left( {4x - 3} \right)^2} - 5x - 2 = 0\\
\Leftrightarrow \left( {4x + 3 - 4x + 3} \right)\left( {4x + 3 + 4x - 3} \right) - 5x - 2 = 0\\
\Leftrightarrow 6.8x - 5x - 2 = 0\\
\Leftrightarrow 43x = 2\\
\Leftrightarrow x = \dfrac{2}{{43}}\\
Vậy\,x = \dfrac{2}{{43}}\\
B4)\\
a)A = {x^2} - {y^2}\\
= \left( {x + y} \right)\left( {x - y} \right)\\
= \left( {87 + 13} \right)\left( {87 - 13} \right)\\
= 100.74\\
= 7400\\
b)B = {x^2} - 6xy + {y^2}\\
= {x^2} - 2xy + {y^2} - 4xy\\
= {\left( {x - y} \right)^2} - 4xy\\
= {\left( {13 - 3} \right)^2} - 4.13.3\\
= 100 - 156\\
= - 56\\
c)C = x\left( {x + 2} \right) + y\left( {y - 2} \right) - 2xy + 37\\
= {x^2} + 2x + {y^2} - 2y - 2xy + 37\\
= {x^2} - 2xy + {y^2} + 2\left( {x - y} \right) + 37\\
= {\left( {x - y} \right)^2} + 2\left( {x - y} \right) + 37\\
= {7^2} + 2.7 + 37\\
= 100\\
d)D = {x^2} + 4{y^2} - 2x + 10 + 4xy - 4y\\
= {x^2} + 4xy + 4{y^2} - 2\left( {x + 2y} \right) + 10\\
= {\left( {x + 2y} \right)^2} - 2\left( {x + 2y} \right) + 10\\
= {5^2} - 2.5 + 10\\
= 25
\end{array}$
