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Find x in terms of a, b and c:2cx#a,b,c |
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Answer» given,a/(x-a) + b/(x-b) = 2c/(x-c)[a(x-b)+b(x-a)]/(x-a)(x-b) = 2c/(x-c) (x-c)[a(x-b)+b(x-a)] = 2c(x-a)(x-b) ax^2 – 2abx + bx^2 - acx + 2abc – bcx = 2cx^2 – 2bcx – 2acx + 2abc ax^2+ bx^2 - 2cx^2 = 2abx – acx – bcx (a+b-2c)x^2 = x(2ab – ac – bc)(a+b-2c)x^2 - x(2ab – ac – bc) = 0 x[(a+b-2c)x - (2ab – ac – bc)] = 0 x = 0 or (a+b-2c)x - (2ab – ac – bc) = 0 x = 0 or (a+b-2c)x = (2ab – ac – bc) x = 0 or x = (2ab – ac – bc) / (a+b-2c) thus the 2 roots of the given equation are x = 0 and x = (2ab – ac – bc) / (a+b-2c) |
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