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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`
Solution
`|(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)`
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