Given the following three equations: I: 3 x 2 y − 5 2 x − 1 3 y + 2 n + 1 = 0 \text{I: } 3x^2y - \frac{5}{2}x - \frac{1}{3}y + 2^n + 1 = 0 I: 3 x 2 y ...

Question

Given the following three equations:

I: 3x2y52x13y+2n+1=0\text{I: } 3x^2y - \frac{5}{2}x - \frac{1}{3}y + 2^n + 1 = 0
II: 2x2y+1Ax+43y10=0\text{II: } -2x^2y + \frac{1}{A}x + \frac{4}{3}y - 10 = 0
III: x2yAx+yP=0\text{III: } x^2y - Ax + y - P = 0

Where:

  • Equation I + Equation II = Equation III
  • nn is the smallest whole number
  • AA and PP are integers

Which of the following statements is/are true?

  1. AA is a prime number
  2. AA is a factor of PP
  3. Product of AA and 15 equals 32

Choose the correct option:

Options

A.

Only 1 and 3

B.

Only 2

C.

Only 2 and 3

D.

Only 1 and 2

E.

None of these

equationsalgebraquadraticintegerprime numberfactor

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