x05+2k+1=（k+2）x的两根的平方和等于11,求kx²+2k+1=﹙k+2﹚x

x05+2k+1=（k+2）x的两根的平方和等于11,求k
x²+2k+1=﹙k+2﹚x

x²+2k+1=﹙k+2﹚x
x²-﹙k+2﹚x+2k+1=0
x1+x2=(k+2)
x1x2=2k+1
x1^2+x2^2=(x1+x2)^2-2x1x2
=(k+2)^2-2(2k+1)
=k^2+2=11
k^2=9
k=±3