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What is the sum of the roots of equation ...

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motion2020
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What is the sum of the roots of equation ... [#permalink] New post   Updated on: 31 Jul 2021, 06:49
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What is the sum of the roots of equation \((x-3)(x-5)={\frac{3}{(x-4)}}-1\) ?

(A) 12
(B) 11
(C) 10
(D) 9
(E) \(4+ 3^{\frac{1}{3}}\)

OA is E.
Previous value edited from 8 to \(4+ 3^{\frac{1}{3}}\)
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E

Originally posted by motion2020 on 30 Jul 2021, 14:34.
Last edited by motion2020 on 31 Jul 2021, 06:49, edited 2 times in total.
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motion2020
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Re: What is the sum of the roots of equation ... [#permalink] New post   31 Jul 2021, 06:43
motion2020 wrote:
What is the sum of the roots of equation \((x-3)(x-5)={\frac{3}{(x-4)}}-1\) ?

(A) 12
(B) 11
(C) 10
(D) 9
(E) \(4+3^{\frac{1}{3}}\)


\((x-3)(x-5)+1={\frac{3}{(x-4)}}\)
\((x-4) * ((x-3)(x-5) + 1) = 3\), hence x =! 4

\((x-4) * (x^2-5x-3x+15+1) = 3\)
\((x-4)(x-4)^2 = 3\)

\((x-4)^3 = 3\)
\(x = 4+ 3^{\frac{1}{3}}\)

I have edited answer
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Re: What is the sum of the roots of equation ... [#permalink]
31 Jul 2021, 06:43
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