若x^2-4x+1=0,求:x^4+1/x^4的值
问题描述:
若x^2-4x+1=0,求:x^4+1/x^4的值
答
x²-4x+1=0,两边同除x得:x-4+1/x=0即:x+1/x=4(x+1/x)²=x²+2+1/x²=16∴x²+1/x²=14(x²+1/x²)²=x^4+2+1/x^4=196∴x^4+1/x^4=194
若x^2-4x+1=0,求:x^4+1/x^4的值
x²-4x+1=0,两边同除x得:x-4+1/x=0即:x+1/x=4(x+1/x)²=x²+2+1/x²=16∴x²+1/x²=14(x²+1/x²)²=x^4+2+1/x^4=196∴x^4+1/x^4=194