Farina wrote:
\(a^2\) = \(b^2- 1\), and \(b\) is not equal to \(0\)
Quantity A |
Quantity B |
\(a^4\) |
\(b^4+1\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Since \(a^4 = (a^2)^2\), we can rewrite Quantity A as follows:
Quantity A: \((a^2)^2\)
Quantity B: \(b^4+1\)
Substitute:
Quantity A: \((b^2- 1)^2\)
Quantity B: \(b^4+1\)
Expand and simplify Quantity A
Quantity A: \(b^4-2b^2+1\)
Quantity B: \(b^4+1\)
Subtract \(b^4\) and subtract \(1\) from both quantities to get:
Quantity A: \(-2b^2\)
Quantity B: \(0\)
Since \(b^2\) must be positive, we can be certain that \(-2b^2\) is NEGATIVE, which means
Quantity B must be greaterAnswer: B