Question

x的4次方-4x的三次方+12x平方-16x+m是完全平方式,求常数m的值

Answer 1

x^4-4x³+12x²-16x+m

=x^4-4x³+8x²+4x²-16x+m

=(x²)²-2x²[2(x-2)]+4x²-16x+m

∴4x²-16x+m=[2(x-2)]²=4x²-16x+16

∴m=16