Let a+b+c =s and `|{:(s+c,,a,,b),(c,,s+a,,b),(c,,a,,s+b):}|=532` then the value of s is `"____"`

Answer

6

Explanation

Given that
` |{:(s+c,,a,,b),(c,,s+a,,b),(c,,a,,s+b):}|=532`
Applying `C_(1) to C_(1)+C_(2)+C_(3)` we get
`(a+b+c+s) |{:(1,,a,,b),(1,,s+a,,b),(1,,a,,s+b):}|=532`
`rArr 2s |{:(0,,-s,,0),(0,,s,,-s),(1,,a,,s+b):}|=532`
`rArr 2s^(3) =532`
`:. s^(3) =216`
`s=6`