一道数学题``今天中午就要答案了`已知X1,X2是关于方程4X^2-(3M-5)-6M^2=0的俩个实数根,且X1/X2的绝对值=3/2,求 常数M的值
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![一道数学题``今天中午就要答案了`已知X1,X2是关于方程4X^2-(3M-5)-6M^2=0的俩个实数根,且X1/X2的绝对值=3/2,求 常数M的值](/uploads/image/z/1838540-20-0.jpg?t=%E4%B8%80%E9%81%93%E6%95%B0%E5%AD%A6%E9%A2%98%60%60%E4%BB%8A%E5%A4%A9%E4%B8%AD%E5%8D%88%E5%B0%B1%E8%A6%81%E7%AD%94%E6%A1%88%E4%BA%86%60%E5%B7%B2%E7%9F%A5X1%2CX2%E6%98%AF%E5%85%B3%E4%BA%8E%E6%96%B9%E7%A8%8B4X%5E2-%EF%BC%883M-5%EF%BC%89-6M%5E2%3D0%E7%9A%84%E4%BF%A9%E4%B8%AA%E5%AE%9E%E6%95%B0%E6%A0%B9%2C%E4%B8%94X1%2FX2%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%3D3%2F2%2C%E6%B1%82+%E5%B8%B8%E6%95%B0M%E7%9A%84%E5%80%BC)
一道数学题``今天中午就要答案了`已知X1,X2是关于方程4X^2-(3M-5)-6M^2=0的俩个实数根,且X1/X2的绝对值=3/2,求 常数M的值
一道数学题``今天中午就要答案了`
已知X1,X2是关于方程4X^2-(3M-5)-6M^2=0的俩个实数根,且X1/X2的绝对值=3/2,求 常数M的值
一道数学题``今天中午就要答案了`已知X1,X2是关于方程4X^2-(3M-5)-6M^2=0的俩个实数根,且X1/X2的绝对值=3/2,求 常数M的值
有两个不同的实数根
所以(3m-5)^2+96m^2>0
105m^2-30m+25>0
此不等式恒成立
x1+x2=(3m-5)/4
x1*x2=-3m^2/2
|x1/x2|=3/2
所以x1=(3/2)x2或x1=-(3/2)x2
x1=(3/2)x2
分别代入x1+x2=(3m-5)/4
x1*x2=-3m^2/2
(5/2)x2=(3m-5)/4
(3/2)x2^2=-3m^2/2
x2=(3m-5)/10
所以(3/2)[(3m-5)/10]^2=-3m^2/2
[(3m-5)/10]^2+m^2=0
则(3m-5)/10=0,且m=0
不成立
x1=-(3/2)x2
分别代入x1+x2=(3m-5)/4
x1*x2=-3m^2/2
-(1/2)x2=(3m-5)/4
(3/2)x2^2=-3m^2/2
x2=-(3m-5)/2
所以-(3/2)[(3m-5)/2]^2=-3m^2/2
[(3m-5)/2]^2=m^2
(3m-5)/2=m或(3m-5)/2=-m
m=5或m=1
题错
X1和X2异号,故X1/X2的值为-3/2
X1/X2+X2/X1=(X1^2+X2^2)/X1X2
={(x1+x2)^2-2x1x2}/x1x2
=-1/24(3-5/m)^2-2=-3/2-2/3=-13/6
解出m=1或5