数学题·········m为有理数,当K为何值时,x²-4mx+4x+3m²-2m+4k的根为有理数?当a、b为何值时关于x的方程x²+2(a+1)x+3a²+4ab+4b²+2=0

Question

数学题·········
m为有理数,当K为何值时,x²-4mx+4x+3m²-2m+4k的根为有理数?
当a、b为何值时关于x的方程x²+2(a+1)x+3a²+4ab+4b²+2=0

Answer 1

1.△=(-4m+4)²-4(3m²-2m+4k)
=16m²-32m+16-12m²+8m-16k
=4m²-24m+(16-16k)
只有(-24)²-4×4(16-16k)=0,即576-256+256k=0,解得k=-5/4
2.x²+2(a+1)x+3a²+4ab+4b²+2=0
x²+2ax+2x+3a²+4ab+4b²+2=0
(x²+2ax+a²)+(a²+4ab+4b²)+(a²+2x+2)=0