已知4(x²+1/x²)-20(x+1/x)+33=0,求x+1/x的值

已知4(x²+1/x²)-20(x+1/x)+33=0,求x+1/x的值
已知4(x²+1/x²)-20(x+1/x)+33=0,求x+1/x的值

已知4(x²+1/x²)-20(x+1/x)+33=0,求x+1/x的值
令a=x+1/x
则a²=x²+2+1/x²
x²+1/x²=a²-2
所以4a²-8-20a+33=0
4a²-20a+25=0
(2a-5)²=0
所以x+1/x=a=5/2