已知：a=根号2+1分之根号2-1，b=根号2-1分之根号2+1，求a平方+b平方分之a+b+ab的值

显示全部楼层 · 2010-7-26 21:06:29

a＝√2-1／√2+1
b＝√2+1／√2-1
求：a+b+ab／a2+b平方的值

千问 · 2010-7-26 21:06:29

∵a＝(√2-1)／(√2+1)=(√2-1)^2/(√2+1)(√2-1)=3-2√2,b＝√2+1／√2-1=3+2√2,a+b=6ab=1∴(a+b+ab)／(a2+b^2)=(6+1)/[(a+b)^2-2ab]=7/(36-2)=7/34

千问 · 2010-7-26 21:06:29

a=(√2-1)/(√2+1）=(√2-1)^2=3-2√2b=(√2+1)/(√2-1)=(√2+1)^2=3+2√2(a+b+ab)/(a^2+b^2)=[3-2√2+3+2√2+(3-2√2)(3+2√2)]/(9-12√2+8+9+12√2+8）=（6+9-8)/34=7/34