Reducing quadratic equation

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aces021: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Mon Mar 24, 2014 8:17 pm

by aces021 » Thu May 29, 2014 12:22 pm

4x^2=y^2-3^2

Is it possible to take the square root of the right side?

Since they are being subtracted our only option is to put it in this form (y-3)(y+3). We are not allowed to do âˆšy^2-3^2 = y-3. Is this correct?

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Source: Beat The GMAT — Problem Solving | Thu May 29, 2014 12:22 pm

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by Brent@GMATPrepNow » Thu May 29, 2014 12:42 pm

aces021 wrote:4x^2=y^2-3^2

Is it possible to take the square root of the right side?

Since they are being subtracted our only option is to put it in this form (y-3)(y+3). We are not allowed to do âˆšy^2-3^2 = y-3. Is this correct?

You are right.
We cannot take the expression yÂ² - 3Â² and rewrite it as (some expression)(the same expression). Therefore, we can't find a "nice" square root of yÂ² - 3Â²
The best we can do is rewrite it as (y + 3)(y - 3)

Also note that we can easily confirm whether or not âˆš(yÂ² - 3Â²) = (y - 3)
Aside: Since âˆš25 = 5, we know that (5)(5) = 25
Likewise, since âˆš49 = 7, we know that (7)(7) = 49
So, IF âˆš(yÂ² - 3Â²) = (y - 3), then it must be true that (y - 3)(y - 3) = yÂ² - 3Â²
HOWEVER, (y - 3)(y - 3) = yÂ² - 6y + 9
So, âˆš(yÂ² - 3Â²) â‰ (y - 3)

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by Brent@GMATPrepNow » Thu May 29, 2014 12:46 pm

We can also confirm whether or not âˆš(yÂ² - 3Â²) = (y - 3) by plugging in some value of y
Let's plug in y = 4
We get âˆš(4Â² - 3Â²) = (4 - 3)
Evaluate to get: âˆš7 = 1 NOPE
So, âˆš(yÂ² - 3Â²) â‰ (y - 3)

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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by [email protected] » Thu May 29, 2014 8:19 pm

Hi aces021,

Is this equation part of a larger GMAT question or are you just interested in the algebra?

Since we cannot take the square root of both sides, that "math move" would not be part of the solution to whatever question this was included in.

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