SEAMO 2027 - Paper E - SET 06 - Self-study Question 6

It is given that $m$ is a real number not less than $-1$, such that the equation in $x$, $x^2+2(m-2)x+m^2-3m+3=0$, has two distinct real roots $x_1,x_2$. If $x_1^2+x_2^2=6$, find $m$.