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If x^4=29x^2
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26 Jun 2017, 10:12
26 Jun 2017, 10:12
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Question Stats:
72% (02:16) correct
27% (01:44) wrong based on 43 sessions
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This is from Quant test#4 question ID: Q02-33
If \(x^4\) \(=\) \(29x^2\) − \(100\), then which of the following is NOT a product of three possible values of x :
I. -50
II. 25
III. 50
a. I only
b. II only
c. III only
d. I and II only
e. I and III only
If \(x^4\) \(=\) \(29x^2\) − \(100\), then which of the following is NOT a product of three possible values of x :
I. -50
II. 25
III. 50
a. I only
b. II only
c. III only
d. I and II only
e. I and III only
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Re: If x^4=29x^2
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27 Jun 2017, 10:45
27 Jun 2017, 10:45
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saumya17lc wrote:
This is from Quant test#4 question ID: Q02-33
If \(x^4\) \(=\) \(29x^2\) − \(100\), then which of the following is NOT a product of three possible values of x :
I. -50
II. 25
III. 50
a. I only
b. II only
c. III only
d. I and II only
e. I and III only
If \(x^4\) \(=\) \(29x^2\) − \(100\), then which of the following is NOT a product of three possible values of x :
I. -50
II. 25
III. 50
a. I only
b. II only
c. III only
d. I and II only
e. I and III only
At first, we might not recognize that the given equation is a quadratic equation in disguise.
To see this, you must notice that (x^2)^2 = x^4
Now, if we let u = x^2, then we can rewrite the given equation.
We get: u^2 = 29u - 100
Rearrange to get: u^2 - 29u + 100 = 0
Factor to get: (u - 4)(u - 25) = 0
So, either u = 4, or u = 25
At this point, we can replace u with x^2 to get:
Either x^2 = 4, or x^2 = 25
If x^2 = 4, then x = 2 or x = -2
If x^2 = 25, then x = 5 or x = -5
So, there are 4 possible values of x: 2, -2, 5, and -5
Which of the following is NOT a product of three possible values of x :
I. -50
II. 25
III. 50
a. I only
b. II only
c. III only
d. I and II only
e. I and III only
I. 50
(-2)(5)(-5) = 50
Since 50 is possible, we can eliminate A, D and E
III. -50
(2)(5)(-5) = 50
Since -50 is possible, we can eliminate C
NOTE: At this point, we need not examine statement II, since we have already eliminated answer choices A, C, D and E
Answer:
Show: ::
B
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Re: If x^4=29x^2
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26 Jun 2017, 15:11
26 Jun 2017, 15:11
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saumya17lc wrote:
This is from Quant test#4 question ID: Q02-33
If x^4=29x^2-100 , then which of the following is NOT a product of three possible values of x :
-50
25
50
a. I only
b. II only
c. III only
d. I and II only
e. I and III only
According to me the answer should be II only(b)
If x^4=29x^2-100 , then which of the following is NOT a product of three possible values of x :
-50
25
50
a. I only
b. II only
c. III only
d. I and II only
e. I and III only
According to me the answer should be II only(b)
If you solve the expression \(x^4=29x^2 -100\) or \(x^4-29x^2+100=0\) or \(x^2= 25, 4\)
So \(x=5, -5, 2, -2\).
You need to multiply 3 solutions. So clearly B is not possible!
