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# If 1/a^2 + a^2 represents the diameter of circle O and 1/a +

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Manager
Joined: 06 Jul 2007
Posts: 55
If 1/a^2 + a^2 represents the diameter of circle O and 1/a +  [#permalink]

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Updated on: 21 Oct 2013, 08:19
3
26
00:00

Difficulty:

55% (hard)

Question Stats:

68% (01:54) correct 32% (02:35) wrong based on 778 sessions

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If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 3, which of the following best approximates the circumference of circle O?

A. 28
B. 22
C. 20
D. 16
E. 12

Originally posted by somethingbetter on 14 Sep 2007, 10:33.
Last edited by Bunuel on 21 Oct 2013, 08:19, edited 3 times in total.
Renamed the topic and edited the question.
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Joined: 17 Sep 2005
Posts: 823
Re: looks pretty simple , huh!!  [#permalink]

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14 Sep 2007, 10:58
2
3
somethingbetter wrote:
If (1/a^2)+a^2 represents the diameter of circle O and (1/a)+a =3 , which of the following best approximates the circumference of circle O?

a. 28
b. 22
c. 20
d. 16
e. 12

Given that (1/a)+a =3

Square both sides of the equation:
We get,

[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)

Diameter D = (1/a)^2 + a^2
= 7 (From (1))

So Radius = D/2 = 7/2

Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
= 22

So the answer should be B.

- Brajesh
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14 Sep 2007, 11:15
I get 22

(1/a + a) =3

(1/a + a) (1/a +a)=1/a^2 +a^2 +2

9-2=7

7*pi=22
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Re: looks pretty simple , huh!!  [#permalink]

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21 Oct 2013, 06:42
1
b14kumar wrote:
somethingbetter wrote:
If (1/a^2)+a^2 represents the diameter of circle O and (1/a)+a =3 , which of the following best approximates the circumference of circle O?

a. 28
b. 22
c. 20
d. 16
e. 12

Given that (1/a)+a =3

Square both sides of the equation:
We get,

[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)

Diameter D = (1/a)^2 + a^2
= 7 (From (1))

So Radius = D/2 = 7/2

Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
= 22

So the answer should be B.

- Brajesh

Hi,

bumping an old question, but why would you square both sides of the equation...I see that it works, but I don't understand how one would know to do that.
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Joined: 02 Sep 2009
Posts: 51215
Re: looks pretty simple , huh!!  [#permalink]

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21 Oct 2013, 08:22
1
3
AccipiterQ wrote:
b14kumar wrote:
somethingbetter wrote:
If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 3, which of the following best approximates the circumference of circle O?

A. 28
B. 22
C. 20
D. 16
E. 12

Given that (1/a)+a =3

Square both sides of the equation:
We get,

[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)

Diameter D = (1/a)^2 + a^2
= 7 (From (1))

So Radius = D/2 = 7/2

Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
= 22

So the answer should be B.

- Brajesh

Hi,

bumping an old question, but why would you square both sides of the equation...I see that it works, but I don't understand how one would know to do that.

We need to find the value of 1/a^2 + a^2, which is a second degree equation. 1/a + a = 3 is a first degree equation. Squaring seems very natural thing to do.
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Re: If 1/a^2 + a^2 represents the diameter of circle O and 1/a +  [#permalink]

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12 Apr 2016, 08:25
somethingbetter wrote:
If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 3, which of the following best approximates the circumference of circle O?

A. 28
B. 22
C. 20
D. 16
E. 12

circumference = 2*pi*r
we are given that 1/a^2 + a^2 is diameter.

1/a + a = 3 -- take square

1/a^2 + a^2 = 7

hence r = 7/2

circumference = 22
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If 1/a^2 + a^2 represents the diameter of circle O and 1/a +  [#permalink]

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30 Jan 2017, 03:16
somethingbetter wrote:
If $$\frac{1}{a^2} + a^2$$ represents the diameter of circle O and $$\frac{1}{a} + a = 3$$, which of the following best approximates the circumference of circle O?

A. 28
B. 22
C. 20
D. 16
E. 12

$$Circumference = 2πr$$

$$( \frac{1}{a} + a )( \frac{1}{a}+ a ) = \frac{1}{a^2} + 1 + 1 + a^2$$

$$(3)(3) = \frac{1}{a^2}+ a^2 + 2$$

$$\frac{1}{a^2} + a^2 = 7 = Diameter$$

$$Circumference = 2πr = 2π ( \frac{7}{2} ) = 7π = 21.99 ≈ 22$$
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Re: If 1/a^2 + a^2 represents the diameter of circle O and 1/a +  [#permalink]

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21 Feb 2018, 13:15
somethingbetter wrote:
If 1/a^2 + a^2 represents the diameter of circle O and 1/a + a = 3, which of the following best approximates the circumference of circle O?

A. 28
B. 22
C. 20
D. 16
E. 12

Squaring 1/a + a = 3, we have:

(1/a + a)^2 = 3^2

1/a^2 + a^2 + 2 = 9

1/a^2 + a^2 = 7

Since 1/a^2 + a^2 = 7 represents the diameter, the circumference is

7π ≈ 22

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Re: If 1/a^2 + a^2 represents the diameter of circle O and 1/a + &nbs [#permalink] 21 Feb 2018, 13:15
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