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# If g(x) = 3x + sqrt x

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Intern
Joined: 08 Dec 2015
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If g(x) = 3x + sqrt x [#permalink]

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Updated on: 25 Feb 2016, 17:08
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If $$g(x) = 3x + \sqrt {x}$$, what is the value of $$g(d^2 +6d+9)$$?

(Chapter 5, Page 79 - In Action problem #2)

SEO was poor for this question. Also, this is more open ended practice so it's less GMAT like.

Originally posted by jwam2 on 25 Feb 2016, 15:31.
Last edited by ENGRTOMBA2018 on 25 Feb 2016, 17:08, edited 1 time in total.
Reformatted the question
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Joined: 02 Aug 2009
Posts: 6235
Re: If g(x) = 3x + sqrt x [#permalink]

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25 Feb 2016, 19:23
jwamala wrote:
If $$g(x) = 3x + \sqrt {x}$$, what is the value of $$g(d^2 +6d+9)$$?

(Chapter 5, Page 79 - In Action problem #2)

SEO was poor for this question. Also, this is more open ended practice so it's less GMAT like.

Hi,
1)$$g(x) = 3x + \sqrt {x}$$..
and $$g(d^2 +6d+9)$$..
so substitute x as d^2 +6d+9..
$$g(d^2 +6d+9) = 3(d^2 +6d+9) + \sqrt {d^2 +6d+9}$$..
$$3d^2+18d+27+d+3=3d^2+19d+30$$

or
2)$$3x + \sqrt {x}=\sqrt {x}(3\sqrt {x}+1)$$...
if$$x= d^2 +6d+9$$, $$\sqrt{x}$$=$$\sqrt{(d+3)^2}$$..
$$\sqrt {x}(3\sqrt {x}+1)$$=$$\sqrt{(d+3)^2}(3\sqrt{(d+3)^2}+1)$$..
$$\sqrt{(d+3)^2}(3\sqrt{(d+3)^2}+1)$$...
=$$(d+3)(3d+9+1)=(d+3)(3d+10)$$
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If g(x) = 3x + sqrt x [#permalink]

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25 Feb 2016, 19:54
The solutions suggest that "3d^2 + 17d + 24" is also an answer. I'm not fully convinced so I've posted it here.

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Re: If g(x) = 3x + sqrt x [#permalink]

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25 Feb 2016, 20:15
I see but still not convinced on having a negative root.

Source: MGMAT Chapter 5, Page 79 - In Action problem #2)

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Posts: 6235
Re: If g(x) = 3x + sqrt x [#permalink]

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25 Feb 2016, 20:19
1
jwamala wrote:
I see but still not convinced on having a negative root.

Source: MGMAT Chapter 5, Page 79 - In Action problem #2)

Posted from my mobile device

As per GMAT,
$$\sqrt{9}= 3$$ and not -3..
only if it is given $$\sqrt{9}= |3|$$, you take two values 3 and -3..

there must be some thing else given too to take -ive root as an option..

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Intern
Joined: 08 Dec 2015
Posts: 26
Re: If g(x) = 3x + sqrt x [#permalink]

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25 Feb 2016, 20:23
I agree with you; that's why I posted the question.

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Re: If g(x) = 3x + sqrt x [#permalink]

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18 Aug 2017, 04:10
chetan2u wrote:
jwamala wrote:
I see but still not convinced on having a negative root.

Source: MGMAT Chapter 5, Page 79 - In Action problem #2)

Posted from my mobile device

As per GMAT,
$$\sqrt{9}= 3$$ and not -3..
only if it is given $$\sqrt{9}= |3|$$, you take two values 3 and -3..

there must be some thing else given too to take -ive root as an option..

Is this only as per GMAT or mathematics in General? bunuel?
Math Expert
Joined: 02 Sep 2009
Posts: 47084
Re: If g(x) = 3x + sqrt x [#permalink]

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18 Aug 2017, 04:19
GMP12 wrote:
chetan2u wrote:
jwamala wrote:
I see but still not convinced on having a negative root.

Source: MGMAT Chapter 5, Page 79 - In Action problem #2)

Posted from my mobile device

As per GMAT,
$$\sqrt{9}= 3$$ and not -3..
only if it is given $$\sqrt{9}= |3|$$, you take two values 3 and -3..

there must be some thing else given too to take -ive root as an option..

Is this only as per GMAT or mathematics in General? bunuel?

When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt[4]{x}$$, then the only accepted answer is the positive root.

That is, $$\sqrt{25}=5$$, NOT +5 or -5. Even roots have only a positive value on the GMAT.

In contrast, the equation $$x^2=25$$ has TWO solutions, +5 and -5.
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Re: If g(x) = 3x + sqrt x   [#permalink] 18 Aug 2017, 04:19
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