Identify which of the following equations is NOT equivalent to $36x^2 = y^2 - 9$ .

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36x^2 + 9 = y^2

108x^2 = 3y^2 - 27

36x^2 = (y + 3)(y - 3)

6x = y - 3

Correct

x^2 = (y^2 - 9)/36

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Explanation

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Official Explanation

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Let's analyze the equation given: 36x^2 = y^2 - 9, which can be rearranged to y^2 - 36x^2 = 9. This can also be expressed as (y - 3)(y + 3) = 36x^2. Now, let's evaluate the options: A) 36x^2 + 9 = y^2 can be rearranged to 36x^2 = y^2 - 9, which matches the original equation, so this option is eliminated. B) 108x^2 = 3y^2 - 27 can be simplified by dividing by 3, yielding 36x^2 = y^2 - 9, which is equivalent to the original equation, so…

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Comments

MatheusOct 6

wait why is D wrong? doesn't 6x = y-3 kinda relate since 36x^2 is (6x)^2?

AmandaOct 15

ohhh right, because y-3 could be negative too. thanks!

What this question tests

What it tests

Your ability to manipulate linear and quadratic expressions, substitute unknowns, and solve equations under time pressure.

Common trap

Losing a sign when moving terms across the equals sign, or dividing both sides by a variable that could equal zero.

Identify which of the following equations is NOT equivalent to 36x2=y2−936x^2 = y^2 - 936x2=y2−9.