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<Text-field style="Heading 1" layout="Normal">identidades de Newton,</Text-field>
<Text-field style="Text" layout="Normal"><Font italic="true">s.</Font><Font encoding="UTF-8"> a f\303\263rmula expressando as pot\303\252ncias das somas das raizes de um polin\303\264mio em termos dos coeficientes do polin\303\264mio. Se </Font></Text-field>
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e </Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> + ... + <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobXN1YnN1cEdGJDYnLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRIm5GJ0YyRjUvRjZRJ25vcm1hbEYnLUYvNiVRImtGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUvc3Vic2NyaXB0c2hpZnRHRkRGPQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkobXN1YnN1cEdGJDYnLUkjbWlHRiQ2JVEickYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUYvNiVRIm5GJ0YyRjUvRjZRJ25vcm1hbEYnLUYvNiVRImtGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUvc3Vic2NyaXB0c2hpZnRHRkRGPQ==</Equation>, 
onde  <Font italic="true">r</Font><Font subscript="true">1</Font>,..., <Font italic="true">r<Font subscript="true">k</Font></Font><Font encoding="UTF-8">  s\303\243o as raizes do polin\303\264mio, ent\303\243o, para  </Font><Font italic="true">k</Font> <Font family="MaplePi">&lt;</Font> <Font italic="true">n</Font> </Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRictRiM2KS1JJW1zdWJHRiQ2JS1GLDYlUSJzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiQtRiw2JVEia0YnRjdGOi9GO1Enbm9ybWFsRicvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JI21vR0YkNi1RIitGJ0ZCLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZNLyUpc3RyZXRjaHlHRk0vJSpzeW1tZXRyaWNHRk0vJShsYXJnZW9wR0ZNLyUubW92YWJsZWxpbWl0c0dGTS8lJ2FjY2VudEdGTS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRmZuLUYjNiYtRjI2JUY0LUYjNiZGKy1GIzYmRj8tRkg2LVEoJm1pbnVzO0YnRkJGS0ZORlBGUkZURlZGWEZaRmduLUkjbW5HRiQ2JFEiMUYnRkJGQkYrRkJGRC1GSDYtUTEmSW52aXNpYmxlVGltZXM7RidGQkZLRk5GUEZSRlRGVkZYL0ZlblEmMC4wZW1GJy9GaG5GXHAtRjI2JS1GLDYlUSJhRidGN0Y6LUYjNiRGZG9GQkZERkJGRy1GIzYmLUYyNiVGNC1GIzYmRistRiM2JkY/RmFvLUZlbzYkUSIyRidGQkZCRitGQkZERmhvLUYyNiVGYHAtRiM2JEZdcUZCRkRGQkYrRkJGK0ZC">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</Equation> + ... + <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> 
enquanto que, para  <Font italic="true">k</Font> <Font family="MaplePi" encoding="UTF-8">\302\263</Font> <Font italic="true">n</Font> </Text-field>
<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> + ... + <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> 
Isto pode ser visto como expressar cada  <Font italic="true">s<Font subscript="true">k</Font></Font>  em termos de <Hyperlink linktarget="Dictionary:Definition/symmetricfunction" hyperlink="true"><Font style="Dictionary Hyperlink" family="Times New Roman" encoding="UTF-8">fun\303\247\303\265es sim\303\251tricas</Font></Hyperlink> elementares.</Text-field>
</Worksheet>