数学数学数学a-b=b-c=3⼀5,a^2+b^2+c^2=1,求ab+bc+ac

a-b=b-c=3/5,a^2+b^2+c^2=1,求ab+bc+ac求简单过程
2025-06-20 16:15:24
推荐回答(1个)
回答1:

∵ a-b=3/5
∴ a=3/5+b
∵ b-c=3/5
∴ b=3/5+c
∴ a-c=6/5
∴ c=a-6/5
ab+bc+ac=(3/5+b)b+(3/5+c)c+a(a-6/5)
= a^2 + b^2 + c^2-6/5a+3/5b+3/5c
=1-3/5a+3/5b-3/5a+3/5c
=1-3/5(a-b)-3/5(a-c)
=1-3/5*3/5-3/5*6/5
=-2/25