2880=576k²/(k²-3)²+144k²/k²-3,求K

2880=576k²/(k²-3)²+144k²/k²-3,求K
2880=576k²/(k²-3)²+144k²/k²-3,求K

2880=576k²/(k²-3)²+144k²/k²-3,求K
2880=576k²/(k²-3)²+144k²/(k²-3)
两边同除以144得
20=4k²/(k²-3)²+k²/(k²-3)
右边通分化简
20=4k²/(k²-3)²+(k^4-3k²)/(k²-3)²
20(k²-3)²=k^4+k²
19k^4-121k²+180=0
(19k-45)(k-4)=0
解得k=45/19或者k=4