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655-705 (Hard)|   Algebra|      
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Bunuel
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The sum of two numbers is 1 and their product is -1. What is the sum 04 Jan 2024, 02:30
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Difficulty:

65% (hard)

Question Stats:

58% (01:54) correct 42% (02:29) wrong based on 263 sessions

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The sum of two numbers is 1 and their product is -1. What is the sum of their cubes?

A. 1
B. 2
C. 3
D. 4
E. 5


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D
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Maheshkv
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GMAT 1: 610 Q49 V25
GMAT 1: 610 Q49 V25
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The sum of two numbers is 1 and their product is -1. What is the sum 04 Jan 2024, 02:58
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(a+b)^3= a^3+ 3*ab*(a+b)+b^3

substituting the values of a+b and ab would give us the required answer of a^3+b^3
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Raulperez947
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The sum of two numbers is 1 and their product is -1. What is the sum 26 Jan 2024, 18:22
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Maheshkv
(a+b)^3= a^3+ 3*ab*(a+b)+b^3

substituting the values of a+b and ab would give us the required answer of a^3+b^3
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why are you using the formula for (a+b)^3 if they are asking for the sum of x^3 + y^3? I'm not sure if i'm correct
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Bunuel
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The sum of two numbers is 1 and their product is -1. What is the sum 27 Jan 2024, 00:56
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Raulperez947
Maheshkv
The sum of two numbers is 1 and their product is -1. What is the sum of their cubes?

A. 1
B. 2
C. 3
D. 4
E. 5

(a+b)^3= a^3+ 3*ab*(a+b)+b^3

substituting the values of a+b and ab would give us the required answer of a^3+b^3


why are you using the formula for (a+b)^3 if they are asking for the sum of x^3 + y^3? I'm not sure if i'm correct
Show more


Given:
    \(a + b = 1\)


Taking to the third power gives:
    \((a + b)^3 = 1^3\)
    \(a^3 + 3ab(a + b) + b^3 = 1\)

Since given that a + b = 1 and ab = -1, then substituting these into the above gives:
    \(a^3 - 3 + b^3 = 1\)
    \(a^3 + b^3 = 4\)

Answer: D.

Hope it's clear.
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The sum of two numbers is 1 and their product is -1. What is the sum 27 Jan 2024, 08:48
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Thank you!! it's clear
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The sum of two numbers is 1 and their product is -1. What is the sum 15 Jan 2026, 04:15
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