k为何值时，不等式0＜3X^2+
解:∵X^2-X+1=(X-1/2)^2+3/4
∴无论X为何值,X^2-X+1>0
∵0＜3X^2+kX+6/X^2-X+1≤6可化为0＜3X^2+kX+6/X^2-X+1,3X^2+kX+6/X^2-X+1≤6这个不等式组，且X^2-X+1>0
∴在不等式组0＜3X^2+kX+6/X^2-X+1,3X^2+kX+6/X^2-X+1≤6两边同时乘以X^2-X+1得：
3X^2+kX+6>0且3X^2+kX+6≤6*(X^2-X+1)
该不等式组化简得：3X^2+kX+6>0且3X^2-(6+k)X≥0
∵3X^2+kX+6>0
∴k^2-4*3*6<0
∴-6√2全部
解:∵X^2-X+1=(X-1/2)^2+3/4
∴无论X为何值,X^2-X+1>0
∵0＜3X^2+kX+6/X^2-X+1≤6可化为0＜3X^2+kX+6/X^2-X+1,3X^2+kX+6/X^2-X+1≤6这个不等式组，且X^2-X+1>0
∴在不等式组0＜3X^2+kX+6/X^2-X+1,3X^2+kX+6/X^2-X+1≤6两边同时乘以X^2-X+1得：
3X^2+kX+6>0且3X^2+kX+6≤6*(X^2-X+1)
该不等式组化简得：3X^2+kX+6>0且3X^2-(6+k)X≥0
∵3X^2+kX+6>0
∴k^2-4*3*6<0
∴-6√2 收起
