Toán Lớp 6: Bài 1. Tính hợp lí:
a) (-8). 25. (-2) . 4.(-5). 125; b) (-167). 83 + 167.(-17) -30
c) 25.(75 – 49) – 75. (25 – 49); d) (-2021) + (-534) + 307 + 434 + (-207)
e) 1 + 2 – 3 – 4 + 5 + 6 – 7 – 8 +… -399 – 400 + 401 + 402
Bài 2. Tìm số nguyên x, biết:
a) (x -2)(x + 5) = 0; b) (2x – 5)2 = 9;
c) (1 – 3x)3 = -8 d) -8 + = – 3
Bài 3. Tìm số nguyên x, biết:
a) (x -2)(x + 3) < 0; b) (x -3)(4 - x) > 0; c) (x2 – 3)(x2 – 7) < 0
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B1)\\
a)\left( { – 8} \right).25.\left( { – 2} \right).4.\left( { – 5} \right).125\\
= – \left( {8.125} \right).\left( {2.5} \right).\left( {4.25} \right)\\
= – 1000.10.100\\
= – 1000000\\
b)\left( { – 167} \right).83 + 167.\left( { – 17} \right) – 30\\
= 167.\left( { – 83 – 17} \right) – 30\\
= 167.\left( { – 100} \right) – 30\\
= – 16700 – 30\\
= – 16730\\
c)25.\left( {75 – 49} \right) – 75.\left( {25 – 49} \right)\\
= 25.75 – 25.49 – 75.25 + 75.49\\
= 49.\left( { – 25 + 75} \right)\\
= 49.50\\
= 2450\\
d)\left( { – 2021} \right) + \left( { – 534} \right) + 307 + 434 + \left( { – 207} \right)\\
= \left( { – 2021} \right) + \left( { – 534 + 434} \right) + \left( {307 – 207} \right)\\
= – 2021 – 100 + 100\\
= – 2021\\
e)1 + 2 – 3 – 4 + 5 + 6 – 7 – 8 + … – 399 – 400 + 401 + 402\\
= 1 + \left( {2 – 3 – 4 + 5} \right) + \left( {6 – 7 – 8 + 9} \right) + …. + \\
+ \left( {398 – 399 – 400 + 401} \right) + 402\\
= 1 + 0 + 0 + … + 0 + 402\\
= 403\\
B2)a)\left( {x – 2} \right)\left( {x + 5} \right) = 0\\
\Leftrightarrow x – 2 = 0/x + 5 = 0\\
\Leftrightarrow x = 2/x = – 5\\
Vậy\,x = 2;x = – 5\\
b){\left( {2x – 5} \right)^2} = 9\\
\Leftrightarrow \left[ \begin{array}{l}
2x – 5 = 3\\
2x – 5 = – 3
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
2x = 8\\
2x = 2
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 4\\
x = 1
\end{array} \right.\\
Vậy\,x = 4;x = 1\\
c){\left( {1 – 3x} \right)^3} = – 8\\
\Leftrightarrow 1 – 3x = – 2\\
\Leftrightarrow 3x = 3\\
\Leftrightarrow x = 1\\
Vậy\,x = 1\\
d) – 8 + ?? = – 3\\
B3)a)\left( {x – 2} \right)\left( {x + 3} \right) < 0\\
\Leftrightarrow – 3 < x < 2\\
Do:x \in Z\\
\Leftrightarrow x \in \left\{ { – 2; – 1;0;1} \right\}\\
Vậy\,x \in \left\{ { – 2; – 1;0;1} \right\}\\
b)\left( {x – 3} \right)\left( {4 – x} \right) > 0\\
\Leftrightarrow \left( {x – 3} \right)\left( {x – 4} \right) < 0\\
\Leftrightarrow 3 < x < 4\\
Do:x \in Z\\
\Leftrightarrow x \in \emptyset \\
c)\left( {{x^2} – 3} \right)\left( {{x^2} – 7} \right) < 0\\
\Leftrightarrow 3 < {x^2} < 7\\
\Leftrightarrow {x^2} = 4\\
\Leftrightarrow x = 2;x = – 2\\
Vậy\,x = 2;x = – 2
\end{array}$