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10 Sep 2017, 05:37
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If \(x^3 - 4x^2 + 5x -5 = 0\), then \(\frac{x(x - 2)^2}{(5 - x)} =\)
A. -0.5
B. 0.5
C. 1
D. 1.5
E. 2
A. -0.5
B. 0.5
C. 1
D. 1.5
E. 2
10 Sep 2017, 06:37
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The expression \(\frac{x(x - 2)^2}{(5 - x)}\) can be re-written as \(\frac{x(x^2 - 4x + 4)}{(5 - x)}\) = \(\frac{(x^3 - 4x^2 + 4x)}{(5 - x)}\)
It has been given \(x^3 - 4x^2 + 5x -5 = 0\) which can re-written as \(x^3 - 4x^2 + 4x + x - 5 = 0\)
Therefore, \(x^3 - 4x^2 + 4x = 5 - x\)
Substituting this value in the simplified expression, we will get the value as \(\frac{(x^3 - 4x^2 + 4x)}{(5 - x)} = \frac{(5 - x)}{(5 - x)} = 1\)(Option C)
It has been given \(x^3 - 4x^2 + 5x -5 = 0\) which can re-written as \(x^3 - 4x^2 + 4x + x - 5 = 0\)
Therefore, \(x^3 - 4x^2 + 4x = 5 - x\)
Substituting this value in the simplified expression, we will get the value as \(\frac{(x^3 - 4x^2 + 4x)}{(5 - x)} = \frac{(5 - x)}{(5 - x)} = 1\)(Option C)
General Discussion
03 Jul 2019, 09:38
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Bunuel
If \(x^3 - 4x^2 + 5x -5 = 0\), then \(\frac{x(x - 2)^2}{(5 - x)} =\)
A. -0.5
B. 0.5
C. 1
D. 1.5
E. 2
A. -0.5
B. 0.5
C. 1
D. 1.5
E. 2
Can be re-arranged into
X^3 - 4x^2 + 4x + x - 5 = 0
X^3 - 4x^2 + 4x = 5 -x -- I)
Simplify x(x-2)^2 = x(x^2 - 4x + 4) = x^3 - 4x^2 + 4x [ There we go equation one located ]
Hence QA : C
