Question

如果a+b=-1,ab=-3,那么a²+b²=___,1：a+1：b=___，b:a+a:b=___,(a-2)(b-2)=____,拜托详细讲一下

Answer 1

1. a²+b² = (a+b)²-2ab = 7
2. a+b=-1两边同除以ab得 1/a+1/b = 1/3
3. a²+b² = -5两边同除以ab得 b/a+a/b = -7/3
4. (a-2)(b-2) = ab -2a-2b +4
= ab -2(a+b) +4
= 3

Answer 2

(a+b)²=a²+b²+2ab推出1=a²+b²-6推出a²+b²=7
1/a+1/b=a+b/ab=1/3
a/b+b/a=a²+b²/ab=-7/3
(a-2)（b-2）=ab-2(a+b)+4=-3+2+4=3