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ریاضیات پایه و آموزش عالی - تعریف یک جمله ای و تحلیل یک جمله ای نبودن قدرمطلق(با مثال)
 
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تعریف یک جمله ای و تحلیل یک جمله ای نبودن قدرمطلق(با مثال)
دوشنبه 14 فروردین 1396 ساعت 09:13 ب.ظ | | نوشته ‌شده به دست ناصر توحیدپور | ( نظرات )

 
یک جمله ای بر حسب متغیر X به صورت 
axn تعریف می شود که در آن a یک عدد حقیقی و n یک عدد صحیح نامنفی است. a را ضریب عددی می نامند.

اگر یک جمله ای چند متغیر داشته باشد، معمولاً به آن یک جمله ای چند متغیره می گویند.

چرا**|x|(قدر مطلق x) یک جمله ای نیست؟

پاسخ:


به طور کل متغیر در قدر مطلق باشد یک جمله ای نیست.زیرا قدر مطلق فاصله یک نقطه تا مبدا است و شامل بی شمار اعداد حقیقی هست. با توجه به تعریف بالا اگر بتوانید «یک بیان با توان‌های صحیح نامنفی» بیابید کار تمام است،برای قدر مطلق هیچ بیانی که توان صحیح نامنفی باشد نمی‌توانید بیابید.البته با عنایت به تعریف قدرمطلق(کتاب ریاضی سال نهم متوسطه)می توان نشان داد که قدر xبه شکل توان دار گویا (غیر صحیح)درخواهد آمد که با تعریف اصلی باز مغایر می باشد.




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