若m^2+n^2=4mn,求(m^2-n^2)/mn的值.

来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 05:18:01
若m^2+n^2=4mn,求(m^2-n^2)/mn的值.
xN@_ekNV>+τKbԔQ&01iX(Wv: Dws3xuq>`5b.؀AmbƳh;!}?lxg)])F2h,nʸ/vv%[1YTk`yf sdyuLlW`^d1J)5p kh*'ac'YV0v/AeJ΁U^'?DMeg`29f&ui'.^u7 31UDt #FE$@.%FHb$QF}ujW*p \M;`i:-D}. :rjqW_

若m^2+n^2=4mn,求(m^2-n^2)/mn的值.
若m^2+n^2=4mn,求(m^2-n^2)/mn的值.

若m^2+n^2=4mn,求(m^2-n^2)/mn的值.
答：
m^2+n^2=4mn>=0
所以：
(m+n)^2=6mn
(m-n)^2=2mn
两式相乘得：
(m^2-n^2)^2=12(mn)^2
所以：m^2-n^2=±(2√3)mn
所以：
(m^2-n^2)/(mn)=±2√3

∵m^2+n^2=4mn
m^2-2mn+n^2=2mn
(m-n)^2=2mn
∴m-n=±√(2mn)
∵m^2+n^2=4mn
m^2+2mn+n^2=6mn
(m+n)^2=6mn
∴m+n=±√(6mn)
则(m^2-n^2)/mn=(m+n)(m-n)/mn
=±√(2mn)√(6mn)/mn
=±√12
=±2√3

两边同除mn得(m/n)+（n/m)=4令m/n=X即x+1/x=4
(m^2-n^2)/mn将n^2=4mn-m^2带入得
2m/n-4
即2x-4=2(x-2)
x-1/x=4化简为x^2-4x=1 即（x-2）^2=3
解得x-2=正负根号3
则为正负2*3^（1/2）-4

若m-n=4,mn=-1,求（-2mn+2m+3n）-（3mn+2n-2m）-（m+4n+mn） 若m-n=4,mn=-1求(9-2mn+2m+3n)-(3mn+2n-2m)-(m+4n+mn) 若m-n=4,mn=-1,求(-2mn+m+n)-(3mn+5n-5m)-(m+4n-3mn)的值 已知m.n不等于0,若m*2-4mn+4n*2=0,求m+n/m-n 若m^2+n^2=4mn,求(m^2-n^2)/mn的值. 若(1/m)-(1/n)=4,求(2m-3mn-2n)/(m-2mn-n)的值 已知m-n=4,m、n互为倒数求(-2mn+2m+3n)-(3mn+2n-2m)-(m+4m+mn)的值 m-n=7 mn=-5求(3m+5n+4mn)-(2n-4n+6mn) 已知m-n=2,mn=1,求多项式(-2mn+2mn+3n)-(3mn+2n-2m)-(m+4n+mn)的值 已知m-n=2,mn=1,求多项式(-2mn+2mn+3n)-(3mn+2n-2m)-(m+4n+mn)的值 已知m-n=4,mn=2,求多项式（-2mn+2m+3n)-(3mn+2n-2n)-(m+4n+mn)的值 已 知m-n=4,mn=-1,求：（-2mn+2m+3n)-(3mn+2n-2n)-(m+4n+mn)的值 已知m-n=4,mn=2,求多项式（-2mn+2m+3n)-(3mn+2n-2m)-(m+4n+mn)的值. 已知m-n=2,mn=1,求多项式(2mn+2m+3n)-(3mn+2n-2m)-(m+4n+mn)的值 已知m-n=4,mn=-1,求（-2mn+2m+3n)-(3mn+2n-2m)-(m+4n+mn）的值. 已知m-n=4,mn=-1,求（-2mn+2m+3n)-(3mn+2n-2m)-(m+4n+mn)的值 已知m-n=3,mn=-3,求(-m-4n-mn)-(2mn-2m-3n)-(3mn+2n-2m)的值 已知m-n=3,mn=-1,求多项式-2mn+2m+3n-3mn-2n+2m-4n-m-mn的值