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Chứng minh: a. x ² + x + 1 > 0 b. (x – 3)(x – 5) + 2 > 0 c. x ² + y ² + 2xy + 4 > 0 d. 4x – 10 – x ² < 0 e. -x ² + 4x – 5 < 0 f. x ² + 2x + y ² + 1 ≥
Question
Chứng minh:
a. x ² + x + 1 > 0
b. (x – 3)(x – 5) + 2 > 0
c. x ² + y ² + 2xy + 4 > 0
d. 4x – 10 – x ² < 0
e. -x ² + 4x – 5 < 0
f. x ² + 2x + y ² + 1 ≥ 0
g. 4( x – 2 )( x – 1 )( x + 4 )( x + 8 ) +25x ² ≥ 0
giúp vwois ạ plsssss
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Môn Toán
4 years
2020-10-15T17:16:22+00:00
2020-10-15T17:16:22+00:00 1 Answers
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Answers ( )
Giải thích các bước giải:
$\begin{array}{l}
a){x^2} + x + 1 = {\left( {x + \frac{1}{2}} \right)^2} + \frac{3}{4} > 0,\forall x\\
b)\left( {x – 3} \right)\left( {x – 5} \right) + 2 = {x^2} – 8x + 17 = {\left( {x – 4} \right)^2} + 1 > 0,\forall x\\
c){x^2} + {y^2} + 2xy + 4 = {\left( {x + y} \right)^2} + 4 > 0,\forall x,y\\
d)4x – 10 – {x^2} = – \left( {{x^2} – 4x + 10} \right) = – {\left( {x – 2} \right)^2} – 6 < 0,\forall x\\
e) – {x^2} + 4x – 5 = – \left( {{x^2} – 4x + 5} \right) = – {\left( {x – 2} \right)^2} – 1 < 0,\forall x\\
f){x^2} + 2x + {y^2} + 1 = {\left( {x + 1} \right)^2} + {y^2} \ge 0,\forall x,y\\
g)4\left( {x – 2} \right)\left( {x – 1} \right)\left( {x + 4} \right)\left( {x + 8} \right) + 25{x^2}
\end{array}$
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