Chứng minh rằng nếu  a1a22(b1+b2)  thì ít nhất  một trong hai phương trình x2+a1x+b1=0,x2+a2x+b2=0 có nghiệm.
Phương trình x2+a1x+b1=0  có Δ1=a214b1
Phương trình x2+a2x+b2=0
Δ2=a224b2
Xét Δ1+Δ2=a21+a224(b1+b2)2a1a24(b1+b2)

=2[a1a22(b1+b2)] theo giả thiết.
ít nhất một trong hai biệt số Δ1,Δ2 phải dương
ít nhất một trong hai phương trình có nghiệm.

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