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How many unique values of set (a,b) are possible if a and b are intege

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How many unique values of set (a,b) are possible if a and b are intege [#permalink]

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New post 12 Apr 2018, 08:25
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How many unique values of set (a,b) are possible if a and b are integers and \(a^2-b^2=29\)?
(A) 1
(B) 2
(C) 3
(D) 4
(E) indefinite
[Reveal] Spoiler: OA

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Re: How many unique values of set (a,b) are possible if a and b are intege [#permalink]

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New post 12 Apr 2018, 10:57
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chetan2u wrote:
How many unique values of set (a,b) are possible if a and b are integers and \(a^2-b^2=29\)?
(A) 1
(B) 2
(C) 3
(D) 4
(E) indefinite


\(a^2-b^2=29\)
\((a-b)*(a+b)=29\)

since 29 is a prime number... so 29 = 1*29 are the only two prime factors.

Only two possibilities:
\(a+b = 29\)
\(a-b = 1\)

&
\(a+b = 1\)
\(a-b = 29\)

for first on solving a = 15 & b = 14
for second on solving a = 15 & b = -14

Hence we have two unique values for the pair (a,b) : (15,14) & (15,-14)

Hence Option (B) is our answer.

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Gladi
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Re: How many unique values of set (a,b) are possible if a and b are intege [#permalink]

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New post 12 Apr 2018, 21:11
chetan2u wrote:
How many unique values of set (a,b) are possible if a and b are integers and \(a^2-b^2=29\)?
(A) 1
(B) 2
(C) 3
(D) 4
(E) indefinite




a^2−b^2=29
(a−b)∗(a+b)=29*1
for a-b = 1 and a+b=29, a=15 and b=14
since we are dealing with even power of a and b, both +ve and -ve values are to be considered

so value of (a,b) = (15,14), (15,-14), (-15,14), (-15,-14)
hence 4 values Option D
Re: How many unique values of set (a,b) are possible if a and b are intege   [#permalink] 12 Apr 2018, 21:11
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