已知方程(x-3)²+4(x-3)=0的解满足方程2x²-kx+1=0,求k的值
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已知方程(x-3)²+4(x-3)=0的解满足方程2x²-kx+1=0,求k的值
已知方程(x-3)²+4(x-3)=0的解满足方程2x²-kx+1=0,求k的值
已知方程(x-3)²+4(x-3)=0的解满足方程2x²-kx+1=0,求k的值
(x-3)²+4(x-3)=0
x^2-6x+9+4x-12=0
x^2-2x-3=0
(x-3)(x+1)=0
(x-3)=0
x=3
(x+1)=0
x=-1
x=3
2x²-kx+1=0
2*3^2-3k+1=0
3k=19
k=19/3
x=-1
2x²-kx+1=0
2*(-1)^2-(-1)k+1=0
k=-3
解由(x-3)²+4(x-3)=0
即(x-3)(x-3+4)=0
即(x-3)(x+1)=0
即x=3或x=-1
当x=3是2x²-kx+1=0的根
即2*3²-3k+1=0
即k=19/3
当x=-1是2x²-kx+1=0的根
即2*(-1)²-(-1)*k+1=0
即k=-3
即k=19/3或k=-3
(x-3)²+4(x-3)=0
(x-3+4)(x-3)=0
(x+1)(x-3)=0
x=-1或3
将上述值代入2x²-kx+1=0中得,
2+k+1=0或18-3k+1=0
k=-3 或19/3