Question

已知a-b=b-c=五分之三,a的平方+b的平方+c的平方=1则ab+bc+ca的值等于？

Answer 1

a-b=3/5..(1)
b-c=3/5..(2)
(1)+(2)
a-b+b-c=3/5+3/5
a-c=6/5

a-c=3/5+3/5=6/5

[a-b]^2+[a-c]^2+[b-c]^2=2[a^2+b^2+c^2]-2[ab+ac+bc]

[3/5]^2+[6/5]^2+[3/5]^2=2*1-2[ab+ac+bc]

ab+ac+bc=[2-54/25]/2=-2/25

Answer 2

ab+bc+ac=a(a-3/5)+b(b-3/5)+c(c+6/5)
=aa+bb+cc-3/5*(a+b-2c)
=1-3/5(a+b-2c)
=1-3/5(c+6/5+c+3/5-2c)
=1-27/25
=-2/25

Answer 3

a-c=3/5 (a-b)^2=a^2+b^2-2ab=9/25
同理 2(a^2+b^2+c^2)-2（ab+ac+bc)=9/25*3
ab+ac+bc=23/50

Answer 4

(a-b)^2+(b-c)^2+(a-b)(b-c)=a^2+b^2+c^2-ab-bc-ac=9/25
ab+bc+ca=1-9/25=16/25

Answer 5

-2/25