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Solve [[x+a,b,c],[a,x+b,c],[a,b,x+c]]=0

Answer»

Solution :`[[X+a,B,c],[a,x+b,c],[a,b,x+c]]=0`
or, `[[x+a+b+c,b,c],[x+a+b+c,x+b,c],[x+a+b+c,b,x+c]]=0`
`(C_1=C_1+C_2+C_3)`
or, `(x+a+b+c)[[1,b,c],[1,x+b,c],[1,b,x+c]]=0`
or, `(x+a+b+c)[[1,b,c],[0,x,0],[0,-x,x]]=0`
`(R_2~~R_2-R_1,R_3~~R_3-R_2)`
or, (x+a+b+c)[[x,0],[-x,x]]=0`
or, `(x+a+b+c)x^2=0`
or, x=0,x=-(a+b+c)


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