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" (x) "(a)/(x-a)+(b)/(x-b)=(2c)/(x-c),x!...

" (x) "(a)/(x-a)+(b)/(x-b)=(2c)/(x-c),x!=a,b,c

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Long-answer type questions (L.A.) (a)/(x-a)+(b)/(x-b)=(2c)/(x-c)(xnea,b,c) .

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If |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))| = (a - b) (b - c) (c - a) (a + b + c) , where a,b,c are all different, then the determinant |(1,1,1),((x-a)^(2),(x-b)^(2),(x-c)^(2)),((x-b)(x-c),(x-c)(x-a),(x-a)(x-b))| vanishes when a)a + b + c = 0 b) x = (1)/(3) (a + b + c) c) x = (1)/(2) (a + b + c) d) x = a + b + c