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# If a and b are negative and a

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Manager
Joined: 31 Oct 2018
Posts: 79
Location: India
If a and b are negative and a  [#permalink]

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18 Apr 2019, 09:35
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Difficulty:

55% (hard)

Question Stats:

62% (02:36) correct 38% (02:31) wrong based on 42 sessions

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If a and b are negative and $$a^2b^2$$ = 21-4ab then $$a^2$$ = ?

A. (16-4b)/$$b^3$$

B. 28/$$b^3$$

C. 16/($$b^2$$+7b)

D. 49/$$b^2$$

E. 9/$$b^2$$

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Manager
Joined: 21 Feb 2019
Posts: 125
Location: Italy
Re: If a and b are negative and a  [#permalink]

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18 Apr 2019, 12:07
1
$$a^2b^2 = 21 - 4ab$$
$$a^2b^2 + 4ab = 21$$
$$ab(ab + 4) = 21$$

Since 21 = 7 * 3, $$ab$$ must be $$3$$ in order for equation to hold true.
$$a^2 = \frac{21 - 4ab}{b^2} = \frac{9}{b^2}$$. Pick E.
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Senior Manager
Joined: 12 Sep 2017
Posts: 297
If a and b are negative and a  [#permalink]

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18 Apr 2019, 13:23
Hi!

$$a^2b^2$$ = 21-4ab

$$\frac{9}{b^2}b^2 + 4\frac{3}{b}b = 21$$

$$9 + 12 = 21$$

E
Intern
Joined: 24 Jun 2018
Posts: 35
Re: If a and b are negative and a  [#permalink]

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18 Apr 2019, 15:28
1
In the question we are given

a^2b^2=21-4ab
=>a^2b^2+4ab-21=0

Lets try to convert this into the form (x+y)^2=x^2+2xy+y^2

a^2b^2+4ab-21=0
or a^2b^2+4ab=21

Add 4 to both sides, we get

a^2b^2+4ab+4=21+4

=>(ab)^2+4ab+4=25

=>(ab+2)^2=25

=>(ab+2)^2=5^2

=>ab+2=5

=>ab=3

=>a=3/b

=>a^2=9/b^2

Hence option E
Intern
Joined: 01 Oct 2017
Posts: 2
Location: India
GPA: 4
Re: If a and b are negative and a  [#permalink]

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21 Apr 2019, 11:45
For me it is between D and E.
Substituting D and E for a^2 makes LHS = RHS.
Director
Joined: 27 May 2012
Posts: 840
If a and b are negative and a  [#permalink]

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21 Apr 2019, 12:15
1
btrg wrote:
If a and b are negative and $$a^2b^2$$ = 21-4ab then $$a^2$$ = ?

A. (16-4b)/$$b^3$$

B. 28/$$b^3$$

C. 16/($$b^2$$+7b)

D. 49/$$b^2$$

E. 9/$$b^2$$

$$(ab)^2 +4ab-21=0$$, Let ab=x
$$(x)^2 +4x-21=0$$
(x+7)(x-3)=0
x=-7 or x=3 since x=ab , hence
ab=-7 or ab=3 since a and b,both are negative hence
ab=3 or $$a=\frac{3}{b}$$
$$a^2=\frac{9}{b^2}$$
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If a and b are negative and a   [#permalink] 21 Apr 2019, 12:15
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# If a and b are negative and a

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