Question

Use properties of determinants to solve for x:

`|(x+a, b, c),(c, x+b, a),(a,b,x+c)| = 0` and `x != 0` 

Answer 1

`|(x+a, b, c),(c, x+b, a),(a,b,x+c)| = 0` and `x != 0` 

`C_1"/"C_1+(C_2 + C_3)`

`|(x+a+b+c, b, c),(x+a+b+c, x+b, a),(x+a+b+c, b, x+c)| = 0`

`(x + a + b + c) |(1,b,c),(1,x+b,a),(1,b, x+c)| = 0`

`R_1"|"R_1-R_3`

`x+a+b+c|(0,0,-x),(1,x+b,a),(1,b,x+c)| = 0`

`:. (x+a+b+c)[0-0-x(b -x -b)] = 0`

`(x+a+b+c)(x^2) = 0`

`:. x^2 = 0`  or    x + a + b + c = 0

but `x!= 0 `

`:. x = -(a+b+c)`