Correction - Exercice 05 page 180 - Activités algébriques
1ère année secondaire
Activités algébriques
Exercice 05 page 180
1- Calculons la valeur de \(A=a^4-\)\(\frac{5}{3}\)\(a–2\) pour \(a=0\) ; \(a=0,5\)
* Pour \(a=0\)
\(A=0^4-\)\(\frac{5}{3}\)\(\times0–2\) \(\Rightarrow\)
\(A=0-\)\(0–2\) \(\Rightarrow\)
\(A=-2\).
* Pour \(a=0,5\)
\(A={0,5}^4-\)\(\frac{5}{3}\)\(\times{0,5}–2\) \(\Rightarrow\)
\(A=0,0625-\)\(\frac{2,5}{3}\)\(–2\) \(\Rightarrow\)
\(A=0,0625-0,8333-2\) \(\Rightarrow\)
\(A=-2,7708\)
2- Calculons la valeur de \(B=(x+9)(x+1)\) pour \(x=-9\) ; \(x=-\)\(\frac{2}{3}\)
* Pour \(x=-9\)
\(B=(-9+9)(-9+1)\) \(\Rightarrow\)
\(B=(-9+9)(-9+1)\) \(\Rightarrow\)
\(B=(0)(-8)\) \(\Rightarrow\)
\(B=0\).
* Pour \(x=-\)\(\frac{2}{3}\)
\(B=(-\)\(\frac{2}{3}\)\(+9)\) \((-\)\(\frac{2}{3}\)\(+1)\) \(\Rightarrow\)
\(B=(-\)\(\frac{2}{3}\)\(+\)\(\frac{27}{3}\)\()\)\((-\)\(\frac{2}{3}\)\(+\)\(\frac{3}{3}\)\()\) \(\Rightarrow\)
\(B=(\)\(\frac{25}{3}\)\()\)\((-\)\(\frac{1}{3}\)\()\) \(\Rightarrow\)
\(B=\)\(\frac{25}{3}\)\(\).
3- Calculons la valeur de \(C=2x^2+7(x-2)–\)\(\frac{3}{2}\)\((1+y)\) pour \(x=-\)\(\frac{2}{3}\) et \(y=2\)
* Pour \(x=-\)\(\frac{2}{3}\) et \(y=2\)
\(C=\)\(2\)\((-\frac{2}{3})^2\)\(+7(\)\(-\frac{2}{3}\)\(-2)–\)\(\frac{3}{2}\)\((1+2)\) \(\Rightarrow\)
\(C=\)\(2\)\((\frac{4}{9})\)\(+7(\)\(-\frac{2}{3}\)\(-\)\(\frac{6}{3}\)\()–\)\(\frac{3}{2}\)\(\times3\) \(\Rightarrow\)
\(C=\)\(\frac{8}{9}\)\(+7(\)\(-\frac{8}{3}\)\()–\)\(\frac{9}{2}\)\(\) \(\Rightarrow\)
\(C=\)\(\frac{8}{9}\)\(-\)\(\frac{56}{3}\)\(–\)\(\frac{9}{2}\)\(\) \(\Rightarrow\)
\(C=\)\(\frac{16}{18}\)\(-\)\(\frac{336}{18}\)\(–\)\(\frac{81}{18}\)\(\) \(\Rightarrow\)
\(C=-\)\(\frac{401}{18}\)
4- Calculons la valeur de \(E=\)\(\frac{25}{4}\)\(x^2-\)\(\frac{35}{3}\)\(xy+\)\(\frac{49}{9}\)\(y^2\) pour \(x=-\)\(\frac{2}{3}\) et \(y=2\)
* pour \(x=-\)\(\frac{2}{3}\) et \(y=2\)
\(E=\)\(\frac{25}{4}\)\((-\frac{2}{3})^2\)\(-\)\(\frac{35}{3}\)\((-\frac{2}{3})\)\(\times2+\)\(\frac{49}{9}\) \(\times2^2\) \(\Rightarrow\)
\(E=\)\(\frac{25}{4}\)\(\times\)\(\frac{4}{9}\)\(-\)\(\frac{35}{3}\)\(\times\)\(-\frac{4}{3}\)\(+\)\(\frac{49}{9}\)\(\times4\)\(\Rightarrow\)
\(E=\) \(\frac{25}{9}\) \(+\) \(\frac{140}{9}\) \(+\) \(\frac{196}{9}\) \(\Rightarrow\)
\(E=\) \(\frac{361}{9}\)
* Pour \(a=0\)
\(A=0^4-\)\(\frac{5}{3}\)\(\times0–2\) \(\Rightarrow\)
\(A=0-\)\(0–2\) \(\Rightarrow\)
\(A=-2\).
* Pour \(a=0,5\)
\(A={0,5}^4-\)\(\frac{5}{3}\)\(\times{0,5}–2\) \(\Rightarrow\)
\(A=0,0625-\)\(\frac{2,5}{3}\)\(–2\) \(\Rightarrow\)
\(A=0,0625-0,8333-2\) \(\Rightarrow\)
\(A=-2,7708\)
2- Calculons la valeur de \(B=(x+9)(x+1)\) pour \(x=-9\) ; \(x=-\)\(\frac{2}{3}\)
* Pour \(x=-9\)
\(B=(-9+9)(-9+1)\) \(\Rightarrow\)
\(B=(-9+9)(-9+1)\) \(\Rightarrow\)
\(B=(0)(-8)\) \(\Rightarrow\)
\(B=0\).
* Pour \(x=-\)\(\frac{2}{3}\)
\(B=(-\)\(\frac{2}{3}\)\(+9)\) \((-\)\(\frac{2}{3}\)\(+1)\) \(\Rightarrow\)
\(B=(-\)\(\frac{2}{3}\)\(+\)\(\frac{27}{3}\)\()\)\((-\)\(\frac{2}{3}\)\(+\)\(\frac{3}{3}\)\()\) \(\Rightarrow\)
\(B=(\)\(\frac{25}{3}\)\()\)\((-\)\(\frac{1}{3}\)\()\) \(\Rightarrow\)
\(B=\)\(\frac{25}{3}\)\(\).
3- Calculons la valeur de \(C=2x^2+7(x-2)–\)\(\frac{3}{2}\)\((1+y)\) pour \(x=-\)\(\frac{2}{3}\) et \(y=2\)
* Pour \(x=-\)\(\frac{2}{3}\) et \(y=2\)
\(C=\)\(2\)\((-\frac{2}{3})^2\)\(+7(\)\(-\frac{2}{3}\)\(-2)–\)\(\frac{3}{2}\)\((1+2)\) \(\Rightarrow\)
\(C=\)\(2\)\((\frac{4}{9})\)\(+7(\)\(-\frac{2}{3}\)\(-\)\(\frac{6}{3}\)\()–\)\(\frac{3}{2}\)\(\times3\) \(\Rightarrow\)
\(C=\)\(\frac{8}{9}\)\(+7(\)\(-\frac{8}{3}\)\()–\)\(\frac{9}{2}\)\(\) \(\Rightarrow\)
\(C=\)\(\frac{8}{9}\)\(-\)\(\frac{56}{3}\)\(–\)\(\frac{9}{2}\)\(\) \(\Rightarrow\)
\(C=\)\(\frac{16}{18}\)\(-\)\(\frac{336}{18}\)\(–\)\(\frac{81}{18}\)\(\) \(\Rightarrow\)
\(C=-\)\(\frac{401}{18}\)
4- Calculons la valeur de \(E=\)\(\frac{25}{4}\)\(x^2-\)\(\frac{35}{3}\)\(xy+\)\(\frac{49}{9}\)\(y^2\) pour \(x=-\)\(\frac{2}{3}\) et \(y=2\)
* pour \(x=-\)\(\frac{2}{3}\) et \(y=2\)
\(E=\)\(\frac{25}{4}\)\((-\frac{2}{3})^2\)\(-\)\(\frac{35}{3}\)\((-\frac{2}{3})\)\(\times2+\)\(\frac{49}{9}\) \(\times2^2\) \(\Rightarrow\)
\(E=\)\(\frac{25}{4}\)\(\times\)\(\frac{4}{9}\)\(-\)\(\frac{35}{3}\)\(\times\)\(-\frac{4}{3}\)\(+\)\(\frac{49}{9}\)\(\times4\)\(\Rightarrow\)
\(E=\) \(\frac{25}{9}\) \(+\) \(\frac{140}{9}\) \(+\) \(\frac{196}{9}\) \(\Rightarrow\)
\(E=\) \(\frac{361}{9}\)
Libellés:
1ère année secondaire
Activités algébriques
Correction
Corrigées
exercice
Le Mathématicien
manuel scolaire
Math
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