已知方程x²-kx-4=0的两根之差的绝对值等于5,则k的值是
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已知方程x²-kx-4=0的两根之差的绝对值等于5,则k的值是
已知方程x²-kx-4=0的两根之差的绝对值等于5,则k的值是
已知方程x²-kx-4=0的两根之差的绝对值等于5,则k的值是
假设A和B为两个根,则根据原题可得A+B=k,a*b=-4,则(a-b)^2=k^2-4ab=k^2+16=25,则k=正负3
x1+x2=k
x1x2=-4
|x1-x2|=5
(x1-x2)²=25
(x1-x2)²=(x1+x2)²-4x1x2
=k²-4(-4)
=k²+16
k²+16=25
k²=9
k=±3