Question

以知(m+n)^2=7,（m-n)^2=3 求m^4+n^4的值

Answer 1

(m+n)^2=7

m^2+n^2+2mn=7

（m-n)^2=3

m^2+n^2-2mn=3

4mn=4

mn=1

m^2+n^2=5

(m^2+n^2)^2=m^4+n^4+2m^2n^2=25

m^4+n^4=25-2=23