(3-k)^2-4*21/2=(k-3)^2-42≥0
(k-3)^2≥42
a+b=k-3
ab=21/2
a^2+b^2=c^2=100
a^2+b^2=(a+b)^2-2ab=k^2-6k+9-21=100
k^2-6k-112=0
(k-14)(k+8)=0
k=14 或k=-8