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For integers a and b, if sqrt(a^3 - a^2 - b) = 7, what is

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For integers a and b, if sqrt(a^3 - a^2 - b) = 7, what is [#permalink] New post 22 Oct 2004, 12:23
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For integers a and b, if sqrt(a^3 - a^2 - b) = 7, what is the value of a?

(1) a^2 - a = 12
(2) b^2 - b = 2


I disagree with the OA so I'd like to others answers ...
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ans [#permalink] New post 22 Oct 2004, 12:33
answer is B.

solving we get b = 2, -1

so (a^2)(a-1) = 51 or (a^2)(a-1) = 48

only 2nd eqn [(a^2)(a-1) = 48] holds as it has valid answer a = 4.
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 [#permalink] New post 22 Oct 2004, 12:49
OA is B.

How does one solve

a^2(a-1) = 48 or a^2(a-1) = 51?
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 [#permalink] New post 22 Oct 2004, 12:54
plug and play we have near values a, a-1.

get the factors of 51 and 48 and check whether they fit and then hit the jackpot.
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  [#permalink] 22 Oct 2004, 12:54
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For integers a and b, if sqrt(a^3 - a^2 - b) = 7, what is

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