已知m-n=3,mn=1,求m^2+n^2的值

来源：百度知道 编辑：UC知道 时间：2024/06/26 03:45:44
（1)已知m-n=3,mn=1,求m^2+n^2的值
(2)(-1/2)^2-2/3×9/8+2^0+(-1)^3+(4/3)^-1
(3)(1/4a^2b)(-2ab^2)^2÷(-0.5a^4b^5)
(4)化简，求值
（x+y)(x-y)+(x-y)^2-(6x^2y-2xy^2)÷2y其中x=2,y=1

(1)mn=1
m-n=3
两边平方
m^2-2mn+n^2=9
所以m^2+n^2=9+2mn=9+2*1=11

(2)(-1/2)^2-2/3×9/8+2^0+(-1)^3+(4/3)^-1
=1/4-3/4+1+(-1)+3/4
=1/4

(3)(1/4a^2b)(-2ab^2)^2÷(-0.5a^4b^5)
=(-1/2a^3b^3)÷(-0.5a^4b^5)
=1/(ab^2)

(4)（x+y)(x-y)+(x-y)^2-(6x^2y-2xy^2)÷2y
=x^2-y^2+x^2-2xy+y^2-3x^2+xy
=-x^2-xy
=-2^2-2*1
=-6

(m-n)^2=9
m^2+n^2-2mn=9

m^2+n^2=9+2mn=9+2=11