设这4个数为,a,aq,aq^2,2aq^2-aq,
则,
19=a+aq+aq^2,
15=aq+aq^2+2aq^2-aq=3aq^2,aq^2 = 5.a = 5/q^2,
19 = a+aq+aq^2 = a+aq+5 = a(1+q)+5=5(1+q)/q^2 + 5,
0 = 14q^2 - 5q - 5,
Delta = 5^2 + 4*5*14=25+280=305,
q = [5+(305)^(1/2)]/28 或 q = [5-(305)^(1/2)]/28.
q^2 = [330+10(305)^(1/2)]/(28*28)或q^2 = [330-10(305)^(1/2)]/(28*28)
a = 5/q^2 = 5*28*28/[330+10(305)^(1/2)] = 14*28/[33+(305)^(1/2)]=[33-(305)^(1/2)]/2
或 a = 14*28/[33-(305)^(1/2)] = [33+(305)^(1/2)]/2
这4个数为[33-(305)^(1/2)]/2,[(305)^(1/2)-5]/2,5,10-[(305)^(1/2)-5]/2=[25-(305)^(1/2)]/2,
或,
[33+(305)^(1/2)]/2,[-(305)^(1/2)-5]/2,5,10+[(305)^(1/2)+5]/2=[25+(305)^(1/2)]/2