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fozzzy
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Which of the following is equal to Updated on: 29 Jun 2013, 00:11
Originally posted by fozzzy on 28 Jun 2013, 23:12.
Last edited by fozzzy on 29 Jun 2013, 00:11, edited 4 times in total.
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B
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62% (02:02) correct 38% (02:17) wrong based on 192 sessions

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If \(x\leq{2}\), Which of the following is equal to \(\sqrt{28x^2 - 112x + 112}\)

A. \(2(x+2) \sqrt{7}\)
B. \(-2\sqrt{7}(x-2)\)
C. \(7(x-2)\)
D. \(14(x-2)\)
E. \(-2 \sqrt{(7x^2 + 28x+28)}\)

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Really confused why the answer is B I solved till it was \(2 \sqrt{7}( x-2)\)

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B
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Bunuel
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Which of the following is equal to 28 Jun 2013, 23:26
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fozzzy
Which of the following is equal to \(\sqrt{28x^2 - 112x + 112}\)

A. \(2(x+2) \sqrt{7}\)
B. \(-2(x-2) \sqrt{7}\)
C. \(7(x-2)\)
D. \(14(x-2)\)
E. \(-2 \sqrt{(7x^2 + 28x+28)}\)

Show Spoiler
Really confused why the answer is B I solved till it was \(7 \sqrt{2}( x-2)\)
Show more

There is no correct answer among the choices.

\(\sqrt{28x^2 - 112x + 112}=\sqrt{28(x^2-4x+4)}=\sqrt{28(x-2)^2}=2\sqrt{7}|x-2|\).
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Which of the following is equal to 28 Jun 2013, 23:32
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fozzzy
Which of the following is equal to \(\sqrt{28x^2 - 112x + 112}\)

A. \(2(x+2) \sqrt{7}\)
B. \(-2(x-2) \sqrt{7}\)
C. \(7(x-2)\)
D. \(14(x-2)\)
E. \(-2 \sqrt{(7x^2 + 28x+28)}\)

Show Spoiler
Really confused why the answer is B I solved till it was \(7 \sqrt{2}( x-2)\)
Show more

\(\sqrt{28x^2 - 112x + 112}\)
= \(\sqrt{28(x^2 - 4x + 4)}\)
= \(\sqrt{4*7(x-2)^2}\)
= \(2*absolute value(x - 2)\sqrt{7}\)

There are two cases:
Case #1: \((x - 2) > 0\) ==> \(2(x - 2)\sqrt{7}\)
Case #2: \((x - 2) < 0\) ==> \(2(2 - x)\sqrt{7}\) = \(-2(x - 2)\sqrt{7}\)

B is the second case, hence B is the only option available ==> I picked B

But I don't think this question is good. My reason is like Bunnel's answer above. The absolute value should be used.
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Which of the following is equal to 28 Jun 2013, 23:46
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fozzzy
Which of the following is equal to \(\sqrt{28x^2 - 112x + 112}\)

A. \(2(x+2) \sqrt{7}\)
B. \(-2(x-2) \sqrt{7}\)
C. \(7(x-2)\)
D. \(14(x-2)\)
E. \(-2 \sqrt{(7x^2 + 28x+28)}\)

Show Spoiler
Really confused why the answer is B I solved till it was \(7 \sqrt{2}( x-2)\)

\(\sqrt{28x^2 - 112x + 112}\)
= \(\sqrt{28(x^2 - 4x + 4)}\)
= \(\sqrt{4*7(x-2)^2}\)
= \(2*absolute value(x - 2)\sqrt{7}\)

There are two cases:
Case #1: \((x - 2) > 0\) ==> \(2(x - 2)\sqrt{7}\)
Case #2: \((x - 2) < 0\) ==> \(2(2 - x)\sqrt{7}\) = \(-2(x - 2)\sqrt{7}\)

B is the second case, hence B is the only option available ==> I picked B

But I don't think this question is good. My reason is like Bunnel's answer above. The absolute value should be used.
Show more

For x=3 (basically for any x which is greater than 2) option B becomes negative, which cannot be correct since square root cannot give negative result.
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Which of the following is equal to 28 Jun 2013, 23:52
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I edited the answer choice if this question was an official question could we expect a condition in the initial statement such as

X>0 or X<0 if not there would be a modulus option in the answer choice?
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Which of the following is equal to 28 Jun 2013, 23:57
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Bunuel
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fozzzy
Which of the following is equal to \(\sqrt{28x^2 - 112x + 112}\)

A. \(2(x+2) \sqrt{7}\)
B. \(-2(x-2) \sqrt{7}\)
C. \(7(x-2)\)
D. \(14(x-2)\)
E. \(-2 \sqrt{(7x^2 + 28x+28)}\)

Show Spoiler
Really confused why the answer is B I solved till it was \(7 \sqrt{2}( x-2)\)

\(\sqrt{28x^2 - 112x + 112}\)
= \(\sqrt{28(x^2 - 4x + 4)}\)
= \(\sqrt{4*7(x-2)^2}\)
= \(2*absolute value(x - 2)\sqrt{7}\)

There are two cases:
Case #1: \((x - 2) > 0\) ==> \(2(x - 2)\sqrt{7}\)
Case #2: \((x - 2) < 0\) ==> \(2(2 - x)\sqrt{7}\) = \(-2(x - 2)\sqrt{7}\)

B is the second case, hence B is the only option available ==> I picked B

But I don't think this question is good. My reason is like Bunnel's answer above. The absolute value should be used.

For x=3 (basically for any x which is greater than 2) option B becomes negative, which cannot be correct since square root cannot give negative result.
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I absolutely agree with you. To be correct, the question should include more information about values of x or change the answers with absolute value added.
Thanks Bunuel.
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Which of the following is equal to 28 Jun 2013, 23:59
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fozzzy
I edited the answer choice if this question was an official question could we expect a condition in the initial statement such as

X>0 or X<0 if not there would be a modulus option in the answer choice?
Show more

\(\sqrt{28x^2 - 112x + 112}\) equals to \(2\sqrt{7}|x-2|\).

If the question were: If \(x\leq{2}\), then which of the following is equal to \(\sqrt{28x^2 - 112x + 112}\)?, then the answer would be \(\sqrt{28x^2 - 112x + 112}=\sqrt{28(x^2-4x+4)}=\sqrt{28(x-2)^2}=2\sqrt{7}|x-2|=-2\sqrt{7}(x-2)\).

Hope it's clear.
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Which of the following is equal to 30 Jun 2013, 11:39
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fozzzy
If \(x\leq{2}\), Which of the following is equal to \(\sqrt{28x^2 - 112x + 112}\)

A. \(2(x+2) \sqrt{7}\)
B. \(-2\sqrt{7}(x-2)\)
C. \(7(x-2)\)
D. \(14(x-2)\)
E. \(-2 \sqrt{(7x^2 + 28x+28)}\)

Show Spoiler
Really confused why the answer is B I solved till it was \(2 \sqrt{7}( x-2)\)
Show more

Plugging numbers is one of the easiest ways to solve this kind of problem.
Let X=1 which satisfies [x<=2]
I choose 1 because inside square root +112 and -112 will cancel off if we do so.
Now, Sqrt root(28*1^2 -112*1 +112*1)=> sqrt (28) i.e 2 sqrt(7)

Try find sqrt in the option choices when x=1.

Lets check Option B:
-2 sqrt(7)(x-2)=> -2 sqrt(7)* (1-2)=> 2 sqrt (7)

I hope my words are clear and convey what I intended to do.

Regards,
AP
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Which of the following is equal to 08 Jun 2016, 22:57
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