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If x^4=29x^2−100, then which of the following is NOT a
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24 Jul 2020, 19:47
24 Jul 2020, 19:47
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Question Stats:
50% (01:46) correct
50% (02:02) wrong based on 16 sessions
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If x^4=29x^2−100, then which of the following is NOT a product of three possible values of x?
Indicate all such values.
A. -50
B. 25
C. 50
Indicate all such values.
A. -50
B. 25
C. 50
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Re: If x^4=29x^2−100, then which of the following is NOT a
[#permalink]
24 Jul 2020, 21:46
24 Jul 2020, 21:46
1
\(x^4\) = \(29x^2\)−100
Take all terms to left hand side we will have
\(x^4 - 29x^2\) + 100 = 0
Let's assume \(x^2\) = y to make the problem look easier
=> \(x^4\) = \({x^2}^2\) = \(y^2\)
=> \(y^2\) - 29y + 100 = 0
=> \(y^2\) - 25y - 4y + 100 = 0
=> y (y-25) - 4(y-25) = 0
=> (y-25) * (y-4) = 0
=> y = 4, 25
=> \(x^2\) = 4 or \(x^2\) = 25
=> x = -2,2 or x = -5,5
Now let's see which all values of x can we use to get product of three of them as the option choice
A. -50 , x can be -5 , 5 and 2 to give product as -50
B. 25 , no combination of 3 values out of {-5,-2,2,5} will give us 25 value so this is the answer
C. 50 , , x can be -5 , -2 and 5 to give product as 50
So, Answer will be B
Hope it helps!
Take all terms to left hand side we will have
\(x^4 - 29x^2\) + 100 = 0
Let's assume \(x^2\) = y to make the problem look easier
=> \(x^4\) = \({x^2}^2\) = \(y^2\)
=> \(y^2\) - 29y + 100 = 0
=> \(y^2\) - 25y - 4y + 100 = 0
=> y (y-25) - 4(y-25) = 0
=> (y-25) * (y-4) = 0
=> y = 4, 25
=> \(x^2\) = 4 or \(x^2\) = 25
=> x = -2,2 or x = -5,5
Now let's see which all values of x can we use to get product of three of them as the option choice
A. -50 , x can be -5 , 5 and 2 to give product as -50
B. 25 , no combination of 3 values out of {-5,-2,2,5} will give us 25 value so this is the answer
C. 50 , , x can be -5 , -2 and 5 to give product as 50
So, Answer will be B
Hope it helps!
gmatclubot
Re: If x^4=29x^2−100, then which of the following is NOT a [#permalink]
24 Jul 2020, 21:46
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