यदि a+b+c=0, तब `|{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0` का हल है -

Options

A. `x = a`
B. `x = (sqrt(3(a^(2) + b^(2) c^(2))))/(2)`
C. `x = (sqrt(2(a^(2)+b^(2)+c^(2))))/(3)`
D. x = 0

Explanation

दिया है,
`|{:(a-x, c,b),(c,b-x,a),(b,c,c-x):}| = 0`
`R_(1) rarr R_(1) + R_(2) + R_(3)`
`|{:(a+b +c-x, a+b+c-x,a+b+c-x),(c,b-x,a),(b,a,c-x):}|=0`
`rArr |{:(-x,-x,-x),(-c,b-x,a),(b,a,c-x):}|`
`[ :' a + b+c = 0]`
`rArr -x|{:(1,1,1),(c,b-x,a),(b,a,c-x):}|=0`
`rArr x = 0`
अतः `x = 0` एक हल है