Question

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£¨1£©$\frac{\sqrt{2}}{\sqrt{2}-1}$x+$\frac{1}{\sqrt{2}+1}$=2x+1
£¨2£©$\left\{\begin{array}{l}{\sqrt{2}x-\sqrt{3}y=\sqrt{2}+\sqrt{3}}\\{\sqrt{3}x-\sqrt{2}y=\sqrt{2}-\sqrt{3}}\end{array}\right.$£®

Answer 1

·ÖÎö £¨1£©ÏȽ«·ÖĸÓÐÀí»¯£¬Ôٽⷽ³Ì¼´¿É½â´ð±¾Ì⣻
£¨2£©¸ù¾Ý¼Ó¼õÏûÔª·¨½â·½³Ì×é¼´¿É½â´ð±¾Ì⣮

½â´ð ½â£º£¨1£©$\frac{\sqrt{2}}{\sqrt{2}-1}$x+$\frac{1}{\sqrt{2}+1}$=2x+1
·ÖĸÓÐÀí»¯£¬µÃ
$\sqrt{2}£¨\sqrt{2}+1£©x+\sqrt{2}-1=2x-1$
È¥À¨ºÅ£¬µÃ
$2x+\sqrt{2}x+\sqrt{2}-1=2x-1$
ÒÆÏî¼°ºÏ²¢Í¬ÀàÏµÃ
$\sqrt{2}x=-\sqrt{2}$
½âµÃ£¬x=-1£»
£¨2£©$\left\{\begin{array}{l}{\sqrt{2}x-\sqrt{3}y=\sqrt{2}+\sqrt{3}}&{¢Ù}\\{\sqrt{3}x-\sqrt{2}y=\sqrt{2}-\sqrt{3}}&{¢Ú}\end{array}\right.$
$¢Ù¡Á\sqrt{2}-¢Ú¡Á\sqrt{3}$£¬µÃ
x=-5
½«x=-5´úÈë¢Ù£¬µÃ
y=-2$\sqrt{6}$-1
¹ÊÔ­·½³Ì×éµÄ½âÊÇ$\left\{\begin{array}{l}{x=-5}\\{y=-2\sqrt{6}-1}\end{array}\right.$£®

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