Solve the following determinant equations: `|(x+a, b, c),( a, x+b, c),( a, b, x+c)|=0` (ii) `|(3x-8, 3, 3),( 3, 3x-8, 3),( 3, 3, 3x-8)|=0`

Explanation

We have given:

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

Now apply `C_1/C_1+(C_2+C_3)`

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

Now apply `R_2->R_2-R_1`

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

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

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