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Which of the following equations is NOT equivalent to 10y^2=

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Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

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New post Updated on: 06 Aug 2012, 10:02
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Which of the following equations is NOT equivalent to 10y^2=(x+2)(x-2)?

A. 30y^2 = 3x^2 - 12
B. 20y^2 = (2x-4)(x+2)
C. 10y^2 + 4 = x^2
D. 5y^2 = x^2 - 2
E. y^2 = (x^2-4)/10


Trying to figure out how you guys would approach this problem:

it's PS: Q37 of OG13 - I searched for it on this forum but no result?

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Originally posted by DelSingh on 06 Aug 2012, 09:57.
Last edited by Bunuel on 06 Aug 2012, 10:02, edited 1 time in total.
Renamed the topic.
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Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

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New post 06 Aug 2012, 10:19
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DelSingh wrote:
Which of the following equations is NOT equivalent to 10y^2=(x+2)(x-2)?

A. 30y^2 = 3x^2 - 12
B. 20y^2 = (2x-4)(x+2)
C. 10y^2 + 4 = x^2
D. 5y^2 = x^2 - 2
E. y^2 = (x^2-4)/10


Trying to figure out how you guys would approach this problem:

it's PS: Q37 of OG13 - I searched for it on this forum but no result?


When \(x=2\), then \(10y^2=(2+2)(2-2)=0\) --> \(y=0\).

Now, plug \(x=2\) into the answer choices and look for the option which does not give \(y=0\). Only option D gives the value of \(y\) different from zero.

Answer: D.

P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html (Rule #3)
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Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

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New post 06 Aug 2012, 11:27
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DelSingh wrote:
Which of the following equations is NOT equivalent to 10y^2=(x+2)(x-2)?

A. 30y^2 = 3x^2 - 12
B. 20y^2 = (2x-4)(x+2)
C. 10y^2 + 4 = x^2
D. 5y^2 = x^2 - 2
E. y^2 = (x^2-4)/10


Trying to figure out how you guys would approach this problem:

it's PS: Q37 of OG13 - I searched for it on this forum but no result?


To practice a little bit of algebra: equivalent equations are obtained by multiplying, dividing a given equation by a non-zero number, or adding, subtracting from both sides the same expression. In other words, after some algebraic manipulations, starting with one equation, we should exactly recover the other equation.
Equivalent equations have the same set of solutions, fact used in his solution by Bunuel. Meaning, for the same value of x, you must get the same value for y in both forms of the equation. Instead of 2, -2 could be used, it also gives y = 0 in the original equation but not in D. It's worth using the zeros of the expression, to avoid spending on computations.

So, the given equation is \(10y^2=(x+2)(x-2)\) (a) or \(10y^2=x^2-4\) (b)

A. \(30y^2 = 3x^2 - 12\) can be obtained from the original equation (b) by multiplying both sides by 3. Therefore equivalent.
B. \(20y^2 = (2x-4)(x+2)=2(x-2)(x+2)\), dividing through by 2 we obtain our original equation (a). Equivalent.
C. \(10y^2 + 4 = x^2\), subtract 4 from both sides, recover the original equation (b). Equivalent.
D. \(5y^2 = x^2 - 2\), multiply both sides by 2, we obtain \(10y^2 = 2x^2 - 4\) and not \(10y^2=x^2-4\). Not equivalent.
E. \(y^2 = (x^2-4)/10\), multiply by 10 both sides, recover equation (b).

Answer D
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Re: Which of the following equations is NOT equivalent to 10y^2=  [#permalink]

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New post 29 Jul 2018, 10:57
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Re: Which of the following equations is NOT equivalent to 10y^2= &nbs [#permalink] 29 Jul 2018, 10:57
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