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
The OA is D.
Experts, what is the best approach to solve this PS question? I'd really appreciate an answer. Thanks.
Hi Vincen,
Let's take a look at your question.
To find out which of the given options is not equivalent to 10y^2=(x+2)(x-2), we will check each option one by one.
The equation $$10y^2=\left(x+2\right)\left(x-2\right)$$ can also be written as,
$$10y^2=x^2-4$$
So the equivalent expressions can be equal to either of the represetation.
Let's start by
Option A.
$$30y^2=3x^2-12$$
$$3\left(10\right)y^2=3\left(x^2-4\right)$$
$$10y^2=x^2-4$$
Which is equivalent to the given expression.
Option B.
$$20y^2=\left(2x-4\right)\left(x+2\right)$$
$$2\left(10\right)y^2=2\left(x-2\right)\left(x+2\right)$$
$$10y^2=\left(x-2\right)\left(x+2\right)$$
Which is equivalent to the given expression.
Option C.
$$10y^2+4=x^2$$
$$10y^2=x^2-4$$
Which is equivalent to the given expression.
Option D.
$$5y^2=x^2-2$$
This expression is not equivalent to the given expression.
Even if we try multiplying the equation by 2, so that we can make 10y^2 at the left side, we will end up with,
$$10y^2=2x^2-4$$
Which is different from the equation given.
Therefore, Option
D is correct.
Hope this helps.
I am available if you'd like any follow up.
