यदि ` |{:( x+a,b,c),(c,x+b,a),(a,b,x+c):}|= 0 ` हो , तो x का मान गया कीजिए ।

Options

A. `abc`
B. `12`
C. `-(a+b+c)`
D. `abc+a+b+c`

Answer

C

Explanation

`rArr |{:(x+a,b,c),(c,x+b,a),(a,b,x+c):}|=0 `
` [ C_(1) to C_(1) + C_(2) +C_(3)]`
` rArr ( x+a+b+c) |{:(1,b,c),(1,x+b,a),(1,b,x+c):}|=0`
` [ C _(1)"से " x+ a +b + c ` उभयनिष्ठ लेने पर ]
` rArr ( x+ a+ b + c) |{:(0,0,-x),(0,x,a-x-c),(1,b,x+c):}|=0 `
` [{:(R_(1) to R_(1) - R_(3)),(R_(2)to R_(2) to R_(3)):}]`
` rArr ( x + a + b + c) [1(0+x^(2))1]=0`
` rArr x + a + b + c = 0 "या " x^(2) = 0 `
` rArr x = -( a+ b+c) "या " x = 0 `