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If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th

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Bunuel
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If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th [#permalink] New post   05 Nov 2014, 08:16
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Tough and Tricky questions: Word Problems.



If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is the value of a^3 – b^3?

A. 1/4
B. 1/2
C. 5/4
D. 7/4
E. 2

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D
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pairakesh10
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Re: If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th [#permalink] New post   06 Nov 2014, 15:19
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Bunuel wrote:

Tough and Tricky questions: Word Problems.



If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is the value of a^3 – b^3?

A. 1/4
B. 1/2
C. 5/4
D. 7/4
E. 2

Kudos for a correct solution.



Give that \(a^3 + b^3 = 8\)
and
\(a^6 - b^6 = 14\)

Solve left hand side:
\((a^3)^2 - (b^3)^2 = 14\)

This is in form \(a^2-b^2\). Hence: \((a^3+b^3) (a^3-b^3) = 14\)

\(8 (a^3-b^3) = 14\)

\((a^3-b^3)=\) 14/8 = 7/4

Answer is D
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Re: If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th [#permalink] New post   06 Nov 2014, 20:41
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Bunuel wrote:

Tough and Tricky questions: Word Problems.



If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is the value of a^3 – b^3?

A. 1/4
B. 1/2
C. 5/4
D. 7/4
E. 2

Kudos for a correct solution.



Given :
\(a^3 + b^3 = 8\) and \(a^6 - b^6 = 14\)

\(a^6 - b^6 = (a^3)^2 - (b^3)^2\)
\(a^6 - b^6 = (a^3 - b^3) (a^3 + b^3)\)

\(14 = (a^3 - b^3) 8\)

\((a^3 - b^3) = 7/4\)

Answer is D
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Re: If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th [#permalink] New post   06 Nov 2014, 02:06
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Bunuel wrote:

Tough and Tricky questions: Word Problems.



If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is the value of a^3 – b^3?

A. 1/4
B. 1/2
C. 5/4
D. 7/4
E. 2

Kudos for a correct solution.


a^3 + b^3 =8 ---------------1)

(a^3)^2-(b^3)^2=14

we know that a^2-b^2 = (a-b)(a+b)
thus
(a^3+b^3)(a^3-b^3) =14
using 1, we have

a^3 - b^3 = 14/8
=7/4
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Re: If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is th [#permalink] New post   31 Aug 2017, 17:46
Bunuel wrote:

Tough and Tricky questions: Word Problems.



If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is the value of a^3 – b^3?

A. 1/4
B. 1/2
C. 5/4
D. 7/4
E. 2

Kudos for a correct solution.


this is just another a sub b question-

(a-b)(a+b) = a^2-b^2

(a^3+b^3)(a^3-b^3)= a^6-b^6= 14

8(a^3-b^3)= 14

(a^3-b^3) = 14/8

d
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Re: If the sum of the cubes of a and b is 8 and a^6 b^6 = 14, what is th [#permalink] New post   30 Mar 2023, 07:49
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Bunuel wrote:

Tough and Tricky questions: Word Problems.



If the sum of the cubes of a and b is 8 and a^6 – b^6 = 14, what is the value of a^3 – b^3?

A. 1/4
B. 1/2
C. 5/4
D. 7/4
E. 2

Kudos for a correct solution.


We know that a^3 + b^3 = 8

We also have that (a^3 + b^3)(a^3 - b^3) = 14. Substituting, we have:

(8)(a^3 - b^3) = 14

a^3 - b^3 = 14/8 = 7/4

Answer D
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Re: If the sum of the cubes of a and b is 8 and a^6 b^6 = 14, what is th [#permalink]
30 Mar 2023, 07:49
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