已知实数a、b、c、d、e、f满足如下方程组2a+b+c+d+e+f=20a+2b+c+d+e+f=40a+b+2c+d+e+f=80a+b+c+2d+e+f

2024-12-28 09:55:47
推荐回答(1个)
回答1:

2a+b+c+d+e+f=20   ①
a+2b+c+d+e+f=40    ②
a+b+2c+d+e+f=80    ③
a+b+c+2d+e+f=160  ④
a+b+c+d+2e+f=320  ⑤
a+b+c+d+e+2f=640  ⑥

∴①+②+③+④+⑤+⑥得:7(a+b+c+d+e+f)=1260,
解得:a+b+c+d+e+f=180⑦,
∴①-⑦得:a=-160,
②-⑦得:b=-140,
③-⑦得:c=-100,
④-⑦得:d=-20,
⑤-⑦得:e=140,
⑥-⑦得:f=460.
∴f-e+d-c+b-a=460-140+(-20)-(-100)+(-140)-(-160)=420.
故答案为:420.