填空和应用,填空要注意1)4x^2+()+y^2=()^22)9x^2+12xy+()=()^23）已知(a+b)^2=9,(a-b)^2=4,求a^2+b^2和ab的值

Question

填空和应用,填空要注意
1)4x^2+( )+y^2=( )^2
2)9x^2+12xy+( )=( )^2
3）已知(a+b)^2=9,(a-b)^2=4,求a^2+b^2和ab的值

Answer 1

1)4x^2+(4xy )+y^2=(2x+y )^2
2)9x^2+12xy+(4y^2 )=(3x+2y )^2
3）已知(a+b)^2=9,(a-b)^2=4,求a^2+b^2和ab的值
由(a+b)^2=9可得：a^2+2ab+b^2=9①
由,(a-b)^2=4可得a^2-2ab+b^2=4②
①+②得：2（a^2+b^2)=13
a^2+b^2=13/2
①-②得：4ab =5
ab=5/4