已知m,n是方程x2-2x-1=0的两根,且(2m2-4m+a)(3n2-6n-7)=8,则a的值等于_.
已知m,n是方程x2-2x-1=0的两根,且(2m2-4m+a)(3n2-6n-7)=8,则a的值等于______.
数学人气:659 ℃时间:2020-03-20 06:00:16
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∵m是方程x2-2x-1=0的两根,∴m2-2m-1=0,∴m2-2m=1,∴2m2-4m=2,∵n是方程x2-2x-1=0的两根,∴n2-2n-1=0,∴n2-2n=1,∴3n2-6n=3,∴(2m2-4m+a)(3n2-6n-7)=8,(2+a)(3-7)=8,2+a=-2,a=-4.故答案为:-4....
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