问一道数学题```初中已知：（m+n)^2=7,（m-n)^2=3,求m^4+n^4的值.过程要详细``````第一个人纯熟胡扯`````
2019-06-02
问一道数学题```初中
已知：（m+n)^2=7,（m-n)^2=3,求m^4+n^4的值.
过程要详细``````第一个人纯熟胡扯`````
优质解答
(m+n)^2=m^2+n^2+2mn=7
(m-n)^2=m^2+n^2-2mn=3
由上两式可得m^2+n^2=5
mn=1
所以,m^4+n^4=(m^2+n^2)^2-2(mn)^2
=25-2
=23
(m+n)^2=m^2+n^2+2mn=7
(m-n)^2=m^2+n^2-2mn=3
由上两式可得m^2+n^2=5
mn=1
所以,m^4+n^4=(m^2+n^2)^2-2(mn)^2
=25-2
=23