Question

已知，4m²-3m-5=0. 5n²＋3n-4=0.其中m,n为实数。求 |m-n分之一|=？

Answer 1

解：原式
=
(m/3)√(3n/m)
/
[(n/2)√(3m
3
/n)]
=
(m/3)√(3n/m)*(2/n)*√(n/3m
3
)
=
(2m/3n)√[(3n/m)(n/3m
3
)]
=
(2m/3n)√(n
2
/m
4
)
=
(2m/3n)*|n/m
2
|
；对n的符号分类讨论可得：
1）如果n
>
0，那么m
>
0，此时原式
=
(2m/3n)*(n/m
2
)
=
2/(3m)
。
2）如果n
<
0，那么m
<
0，此时原式
=
(2m/3n)*(-n/m
2
)
=
-2/(3m)
。