已知a+b=3,ab=2,求a^2+b^2的值和（a-b）^2
已知a+b=3,ab=2,求a^2+b^2的值和（a-b）^2
解：a²+b²
=(a+b)²－2ab
=3²－2×2
=9－4
=5
(a-b)²
=(a+b)²-4ab
=3²-4×2
=9-8
=1
已知a+b=4，ab=3，求a^2+b^2和a-b的值
a²+b²
=a²+b²+2ab-2ab
=(a+b)²-2ab
=16-2*3
=10
(a-b)²
=a²+b²-2ab
=10-6
=4
∴ a-b=2或a-b=-2
a^2+b^2 = (a+b)^2-2ab = 16-6 = 10
(a-b)^2 = a^2+b^2-2ab = 10-6 = 4
所以a-b = 2
已知a+b=3,ab=-2,求a^2+b^2及（a-b）^2的值
解：a²+b²
=(a+b)²-2ab
=3²-2×(-2)
=9+4
=13
(a-b)²
=(a+b)²-4ab
=3²-4×(-2)
=9+8
=17
已知a+b=4,ab=2,求a^2+b^2和(a-b)^2的值
a^2+b^2
=a^2+b^2+2ab-2ab
=(a+b)^2-2ab
=4^2-2×2
=12
(a-b)^2
=a^2+b^2-2ab
=a^2+b^2+2ab-4ab
=(a+b)^2-4ab
=4^2-4×2
=8
已知a-b=5，ab=3，求(a+b)^2与a^2+b^2的值
a-b=5，ab=3
则有(A-B)^2=A^2-2AB+B^2=25
==>A^2+B^2=25+2AB=31
所有(A+B)^2=A^2+B^2+2AB=31+2*3=37
A^2+B^2=31
已知(a+b)^2=10,(a-b)^2=2,求a^2+b^2和ab的值
(a+b)^2=a^2+b^2+2ab=10
(a-b)^2=a^2+b^2-2ab=2
两式相减4ab=8 ab=2
ab=2代入得a^2+b^2=6
已知a-b=3，(a+b)^2=13 (1)求a^2+b^2的值 (2)求ab的值
因为a-b=3，将其平方得(a-b)^2=a^2-2ab+b^2=9 ，又因为(a+b)^2=a^2+2ab+b^2=13 ， 两个式子联立: 1式+2式再除以2得a^2+b^2=11 ， 2式-1式再除以4得ab=1
已知(a-b)=5,ab=3,求(a+b)^2与3(a^2+b^2)的值.
解：(a+b)²=(a-b)²+4ab
=5²+4×3
=25+12
=37
3(a²+b²)=3[(a-b)²+2ab]
=3×(5²+2×3)
=3×(25+6)
=3×31
=93
