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# Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?

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Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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14 Jan 2015, 23:05
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Which of the following equations is NOT equivalent to $$4x^2 = y^2 - 9$$ ?

(A) $$4x^2+ 9 = y^2$$

(B) $$4x^2 - y^2 = -9$$

(C) $$4x^2= (y + 3)(y - 3)$$

(D) $$2x = y - 3$$

(E) $$x^2 = \frac{(y^2 - 9)}{4}$$

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Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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14 Jan 2015, 23:29
Hi abhisheknandy08,

This question is based on the various ways that you're mathematically "allowed" to manipulate an equation. We're asked to find the answer that is NOT the equivalent of the equation in the prompt.

We're given 4X^2 = Y^2 - 9

I'm going to work through the answers, starting with A....

A: If we ADD 9 to both sides, we'd have...
4X^2 + 9 = Y^2
This IS EQUIVALENT.

B: If we SUBTRACT Y^2 from both sides, we'd have....
4X^2 - Y^2 = -9
This IS EQUIVALENT.

C: If we FACTORED the "right side" of the equation, we'd have...
4X^2 = (Y+3)(Y-3)
This IS EQUIVALENT.

D: There's no acceptable math rule we can use to get to this answer.
This is NOT equivalent.

E: If we DIVIDE both sides by 4, we'd have....
X^2 = (Y^2 - 9)/4
This IS EQUIVALENT.

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Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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15 Jan 2015, 01:05
abhisheknandy08 wrote:
Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?

(A) 4x^2 + 9 = y^2
(B) 4x^2 - y^2 = -9
(C) 4x^2= (y + 3)(y - 3)
(D) 2x = y - 3
(E)x^2 = (y^2-9)/4

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Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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15 Jan 2015, 01:16
Could you please elaborate on D..Why is it not possible and what is possible in such a scenario(when an expression has both squares and roots and we want to eliminate them)?I'm having trouble with this concept.
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Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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15 Jan 2015, 20:26
Hi Ralphcuisak,

Here's why you can't re-write/reduce/simplify the prompt to what's listed in Answer D:

We're given.....

4X^2 = Y^2 - 9

The basic rule when dealing with equations is that you can do ANYTHING to both sides of an equation as long as you do it EQUALLY to BOTH sides. Everything gets a bit more complex when you're dealing with variables in the denominator of a fraction and/or inequalities, but neither of those subjects is a factor in this prompt.

Looking at Answer D, we have....

2X = Y - 3

While you COULD take the square root of both sides of the original equation, it's important to note that the square root of Y^2 - 9 is NOT (Y-3).

Y^2 - 9 can be factored into (Y-3)(Y+3), but neither of these parentheses is the square root of Y^2 - 9.

You can see the proof when you square either of the two parentheses:
(Y-3)^2 = Y^2 - 6X + 9
(Y+3)^2 = Y^2 + 6x + 9

Thus, D is NOT equivalent to the prompt.

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Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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17 Jul 2015, 23:59
1
Do we need to tag functions and custom characters in this? I think it is plain algebra with all standard characters (no custom characters)?
abhisheknandy08 wrote:
Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?

(A) 4x^2 + 9 = y^2
(B) 4x^2 - y^2 = -9
(C) 4x^2= (y + 3)(y - 3)
(D) 2x = y - 3
(E)x^2 = (y^2-9)/4

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Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?  [#permalink]

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11 Aug 2019, 19:21
TheKingInTheNorth wrote:
Which of the following equations is NOT equivalent to $$4x^2$$ = $$y^2$$- 9 ?

(A) $$4x^2$$+ 9 = $$y^2$$
(B) $$4x^2$$ - $$y^2$$ = -9
(C) $$4x^2$$= (y + 3)(y - 3)
(D) 2x = y - 3
(E) $$x^2$$ = ($$y^2$$-9)/4

Edit: Formatting

We can always look for number plugging method as well because sometimes equations get difficult to be compared.

Here taking x =2 & y =5 satisfies the equation, plugging the same number in the list of options only D : 2x = y -3 does not satisfy the equation.

Hence D
Re: Which of the following equations is NOT equivalent to 4x^2 = y^2 - 9 ?   [#permalink] 11 Aug 2019, 19:21
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