by: Bunuel
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by: Bunuel
6 mins
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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
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A. -0.5
B. 0.5
C. 1
D. 1.5
E. 2
_________________
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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
Posts: 54
Bunuel
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
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Expert reply
Posts: 22,742
Bunuel
We see that the numerator of the fractional expression is:
x(x^2 - 4x + 4) = x^3 - 4x^2 + 4x
Since x^3 - 4x^2 + 5x - 5 = 0, then x^3 - 4x^2 + 4x + x - 5 = 0, and therefore,
x^3 - 4x^2 + 4x = 5 - x
Thus, the numerator of the fractional expression is really 5 - x, and it is divided by 5 - x (itself), and so the quotient is 1.
Answer: C
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Bunuel
Let's break the numerator as- x(x - 2)^2
we can rewrite it as- (x^3-4x^2+4) ---------(1)
Now we'll break this eq- x^3 - 4x^2 + 5x -5 = 0 and we'll write it as x^3 - 4x^2 + 4x + x-5=0,
x^3 - 4x^2 + 4x=5-x--------(2)
we'll put the eq (2) into eq (1)
5-x/5-x which will be equal to 1.
So the answer is C
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