Question

若x1和x2是一元二次方程x²+x-3=0的两个根,求下列各式的值

1。|x1-x2|
2。x1²+2x1+x2

Answer 1

1。|x1-x2|
=√(x1-x2)²
=√[(x1+x2)²-4x1x2]
=√[(-1)²-4×(-3)]
=√13

2。x²+x-3=0
x1²+x1-3=0
x1²+x1=3

x1²+2x1+x2
=x1²+x1+(x1+x2)
=3-1
=2