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

题目

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

答案

(x-3)²+4(x-3)=0x^2-6x+9+4x-12=0x^2-2x-3=0(x-3)(x+1)=0(x-3)=0x=3(x+1)=0x=-1 x=32x²-kx+1=02*3^2-3k+1=03k=19k=19/3 x=-12x²-kx+1=02*(-1)^2-(-1)k+1=0k=-3