Question

18£®ÔĶÁÏÂÃæµÄÎÄ×Ö£¬½â´ðÎÊÌ⣺´ó¼ÒÖªµÀ$\sqrt{2}$ÊÇÎÞÀíÊý£¬¶øÎÞÀíÊýÊÇÎÞÏÞ²»Ñ­»·Ð¡Êý£¬Òò´Ë$\sqrt{2}$µÄСÊý²¿·ÖÎÒÃDz»¿ÉÄÜÈ«²¿µØд³öÀ´£¬ÓÚÊÇСÃ÷ÓÃ$\sqrt{2}$-1À´±íʾ$\sqrt{2}$µÄСÊý²¿·Ö£¬ÊÂʵÉÏ£¬Ð¡Ã÷µÄ±íʾ·½·¨ÊÇÓеÀÀíµÄ£¬ÒòΪ$\sqrt{1}$£¼$\sqrt{2}$£¼$\sqrt{4}$£¬ËùÒÔ$\sqrt{2}$µÄÕûÊý²¿·ÖÊÇ1£¬½«Õâ¸öÊý¼õÈ¥ÆäÕûÊý²¿·Ö£¬²î¾ÍÊÇСÊý²¿·Ö£®Çë¾Ý´Ë½â´ð£º
£¨1£©$\sqrt{11}$µÄÕûÊý²¿·ÖÊÇ3£¬Ð¡Êý²¿·ÖÊÇ$\sqrt{11}$-3
£¨2£©Èç¹û$\sqrt{7}$µÄСÊý²¿·ÖΪa£¬$\sqrt{41}$µÄÕûÊý²¿·ÖΪb£¬Çóa+b-$\sqrt{7}$µÄÖµ£»
£¨3£©ÈôÉè2+$\sqrt{3}$µÄÕûÊý²¿·ÖΪx£¬Ð¡Êý²¿·ÖΪy£¬Çóy-xµÄÖµ£®

Answer 1

·ÖÎö ¸ù¾Ý¹ÀËãÎÞÀíÊýµÄ´óС£¬¼´¿É½â´ð£®

½â´ð ½â£º£¨1£©¡ß3£¼$\sqrt{11}$£¼4£¬
¡à$\sqrt{11}$µÄÕûÊý²¿·ÖÊÇ3£¬Ð¡Êý²¿·ÖÊÇ$\sqrt{11}$-3£»
¹Ê´ð°¸Îª£º3£»$\sqrt{11}$-3£®
£¨2£©¡ß2£¼$\sqrt{7}$£¼3£¬
¡àa=$\sqrt{7}$-2£¬
¡ß6£¼$\sqrt{41}$£¼7£¬
¡àb=6£¬
¡àa+b-$\sqrt{7}$=$\sqrt{7}$-2+6-$\sqrt{7}$=4£®
£¨3£©¡ß1£¼$\sqrt{3}$£¼2£¬
¡à3£¼2+$\sqrt{3}$£¼4£¬
¡à2+$\sqrt{3}$µÄÕûÊý²¿·ÖΪx=3£¬Ð¡Êý²¿·ÖΪy=2+$\sqrt{3}$-3=$\sqrt{3}$-1£®

µãÆÀ ±¾Ì⿼²éÁ˹ÀËãÎÞÀíÊýµÄ´óС£¬½â¾ö±¾ÌâµÄ¹Ø¼üÊÇÊì¼Ç¹ÀËãÎÞÀíÊýµÄ´óС£®