Question

16£®Èçͼ1£¬¡÷ABCÖУ¬AB=AC£¬¡ÏBAC=90¡ã£¬µãMÊÇBC±ßÉϵÄÒ»¸ö¶¯µã£¬µãB¹ØÓÚµãMµÄ¶Ô³ÆµãNÔÚBCÉÏ£¨Ô˶¯¿ªÊ¼Ê±£¬µãMÓëµãBÖغϣ¬µ±µãNµ½´ïµãCʱÔ˶¯ÖÕÖ¹£©£¬¹ýµãM¡¢N×÷BCµÄ´¹Ïߣ¬ÓëÕÛÏßB¡úA¡úC·Ö±ð½»ÓÚP¡¢QÁ½µã£¬ÉèÏ߶ÎBMµÄ³¤Îªx£¬ËıßÐÎPQNMµÄÃæ»ýΪS£¬S¹ØÓÚxµÄº¯ÊýͼÏóÈçͼ2Ëùʾ£¨ÆäÖÐ0£¼x¡Ü$\frac{3}{2}$£¬$\frac{3}{2}$£¼x¡Üaʱ£¬º¯ÊýµÄ½âÎöʽ²»Í¬£©£®
£¨1£©Ìî¿Õ£ºµ±PM=QNʱ£¬xµÄֵΪ2£»
£¨2£©ÇóS¹ØÓÚxµÄº¯Êý¹Øϵʽ£¬²¢Ð´³öxµÄÈ¡Öµ·¶Î§£®

Answer 1

·ÖÎö £¨1£©ÓÉͼ2¿ÉÖªBC=$\frac{3}{2}$¡Á4=6£¬¼´a=6¡Â2=3£¬¸ù¾ÝPM=QN£¬ÓɶԳƵÄÐÔÖʵõ½¹ØÓÚxµÄ·½³Ì£¬½â·½³Ì¼´¿ÉÇó½â£»
£¨2£©·ÖÁ½ÖÖÇé¿ö£º¢Ù0£¼x¡Ü$\frac{3}{2}$£¬¢Ú$\frac{3}{2}$£¼x¡Ü3£¬½øÐÐÌÖÂÛ¿ÉÇóS¹ØÓÚxµÄº¯Êý¹Øϵʽ£¬²¢Ð´³öxµÄÈ¡Öµ·¶Î§£®

½â´ð ½â£ºÓÉͼ2¿ÉÖªBC=$\frac{3}{2}$¡Á4=6£¬¼´a=6¡Â2=3£¬
£¨1£©ÒÀÌâÒâÓУº
x=6-2x£¬
½âµÃx=2£®
£¨2£©¢Ù0£¼x¡Ü$\frac{3}{2}$£¬S=2x¡Á2x¡Â2-x²¡Â2=$\frac{3}{2}$x²£»
¢Ú$\frac{3}{2}$£¼x¡Ü3£¬S=£¨x+6-2x£©£¨6-x-6+2x£©¡Â2=-$\frac{1}{2}$x²+3x£®
×ÛÉÏËùÊö£¬S¹ØÓÚxµÄº¯Êý¹ØϵʽÊÇS=$\frac{3}{2}$x²£¨0£¼x¡Ü$\frac{3}{2}$£©£»S=-$\frac{1}{2}$x²+3x£¨$\frac{3}{2}$£¼x¡Ü3£©£®
¹Ê´ð°¸Îª£º2£®

µãÆÀ ´ËÌ⿼²éÁ˶¯µãÎÊÌâµÄº¯ÊýͼÏó£¬Éæ¼°µ½µÈÑüÈý½ÇÐεÄÐÔÖÊ£¬¶Ô³ÆµÄÐÔÖÊ£¬Èý½ÇÐεÄÃæ»ý£¬ËıßÐεÄÃæ»ý£¬±È½Ï¸´ÔÓ£®Ò»°ãÔÚ½â¾ö¶¯µãÎÊÌâʱ£¬²ÉÈ¡ÊýÐνáºÏÓë·ÖÀàÌÖÂÛµÄ˼Ï룮