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
Please explain the solution for this problem.
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jayhawk2001
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Using (1), you get a^2 -a - 12 = 0 which implies a = 4 or a = -3.f2001290 wrote: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
Please explain the solution for this problem.
Hence insufficient.
Using (2), b^2 -b -2 = 0 which implies b = 2 or b = -1
a^3 - a^2 - b = 49
a^2(a-1) = 49 + b
We know a(a-1) should be even. so, b = -1
So, a^2(a-1) = 48
Only a=4 satisfies above eqn. sufficient.
Hence B
