Question

已知:(m+n)^2=10，（m-n）^2=2,求m^4+n^4

Answer 1

解：（m+n)^2=10推出 m^2+2mn+n^2=10.....①式
（m-n）^2=2推出 m^2-2mn+n^2=2......②式
①-②=4mn=8推出mn=2
①+②=2(m^2+n^2)=12推出m^2+n^2=6
∴m^4+n^4=（m^2+n^2）^2-2(mn)^2=6^2-2*2^2=28

Answer 2

∵（m+n)2-(m-n)2=m2+2mn+n2-m2+2mn-n2=4mn=8 ∴mn=2
∵(m+n)2×(m-n)2=[(m+n)(m-n)]2
=(m2-n2)2
=m^4-2m2n2+n^4=20
将mn=2带入上式m^4-8+n^4=20
∴m^4+n^4=28

Answer 3

m2+n2+2mn=10
m2-2mn+n2=2
m2+n2=6 → （m2+n2）2=m4+n4+2m2n2=36
m*n=2 → 2m2*n2=8

m4+n4 =144-8=28

Answer 4

(m+n)^2=m^2+n^2+2mn=10
(m-n)^2=m^2+n^2-2mn=2
m^2+n^2=6
mn=2
所以(mn)^2=4
m^4+n^4=(m^2+n^2)^2-2(mn)^2
=36-8=28