Toán Lớp 10: Bài 1 Giải bất pt TAM THỨC BẬC 2
a,-x² + 5x – 4 > 0
b,-x² – 9x + 10 < 0
c,x² - 7x + 6 ≥ 0
d,x² - 10x + 21 ≤ 0
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Toán Lớp 10: Bài 1 Giải bất pt TAM THỨC BẬC 2
a,-x² + 5x – 4 > 0
b,-x² – 9x + 10 < 0
c,x² - 7x + 6 ≥ 0
d,x² - 10x + 21 ≤ 0
Comments ( 1 )
Giải đáp:
a) \(x \in \left( {1;4} \right)\)
b) \(x \in \left( { – \infty ; – 10} \right) \cup \left( {1; + \infty } \right)\)
c) \(x \in \left( { – \infty ;1} \right] \cup \left[ {6; + \infty } \right)\)
d) \(x \in \left[ {3;7} \right]\)
Lời giải và giải thích chi tiết:
\(\begin{array}{l}
a) – {x^2} + 5x – 4 > 0\\
\to \left( {4 – x} \right)\left( {x – 1} \right) > 0
\end{array}\)
BXD:
x -∞ 1 4 +∞
f(x) – 0 + 0 –
\(KL:x \in \left( {1;4} \right)\)
\(\begin{array}{l}
b) – {x^2} – 9x + 10 < 0\\
\to \left( {1 – x} \right)\left( {x + 10} \right) < 0
\end{array}\)
BXD:
x -∞ -10 1 +∞
f(x) – 0 + 0 –
\( \to x \in \left( { – \infty ; – 10} \right) \cup \left( {1; + \infty } \right)\)
\(\begin{array}{l}
c){x^2} – 7x + 6 \ge 0\\
\to \left( {x – 1} \right)\left( {x – 6} \right) \ge 0
\end{array}\)
BXD:
x -∞ 1 6 +∞
f(x) + 0 – 0 +
\( \to x \in \left( { – \infty ;1} \right] \cup \left[ {6; + \infty } \right)\)
\(\begin{array}{l}
d){x^2} – 10x + 21 \le 0\\
\to \left( {x – 7} \right)\left( {x – 3} \right) \le 0
\end{array}\)
BXD:
x -∞ 3 7 +∞
f(x) + 0 – 0 +
\( \to x \in \left[ {3;7} \right]\)