初中数学完全平方公式

Question

(M+N)的平方=7，（m-n)的平方=3求代数式m的四次方+n的四次方

Answer 1

(m+n)^2=m^2+2mn+n^2=7
(m-n)^2=m^2-2mn+n^2=3
得：m^2+n^2=5, mn=1
m^4+n^4=(m^2+n^2)^2-2m^2n^2
=25-2
=23

Answer 2

(m+n)^2-(m-n)^2
=4mn=7-3=4
mn=1
(m+n)^2+(m-n)^2=2(m^2+n^2)=10
m^2+n^2=5

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

=25-2*1=23

Answer 3

(m+n)^2=m^2+2mn+n^2=7
(m-n)^2=m^2-2mn+n^2=3
→m^2+n^2=5, mn=1
m^4+n^4=(m^2+n^2)^2-2m^2n^2
=25-2 =23

Answer 4

(m+n)^2=m^2+n^2+2mn=7,
(m-n)^2=m^2+n^2-2mn=3,
得出mn=1，m^2+n^2=5
(m^2+n^2)^2=m^4+n^4+2m^2n^2,
m^4+n^4=25-2*1^2=23

Answer 5

(M+N)的平方=7,（m-n)的平方=3
m²+n²+2mn=7①
m²+n²-2mn=3②

①-②得 4mn=4
mn=1
①+②得 2（m²+n²）=10
m²+n²=5

（m²+n²）²=m四次方+n的四次方+2m²n²
25=m四次方+n的四次方+2（mn)²
25=m四次方+n的四次方+2
m四次方+n的四次方=23

他们打字速度也忒回了吧，又比我先做完

Answer 6

(m+n)^2=m^2+n^2+2mn=7 (1)
(m-n)^2=m^2+n^2-2mn=3 (2)
(1)式-(2)式得mn=1
将mn=1代入(1)式得m^2+n^2=5
所以m^4+n^4=(m^2+n^2)^2-2(mn)^2=25-2=23
说明：上述^为次的意思。>_<