Final answer:
The possible value of x + y given the equation x^2 = 100y^2 - 16 is 14, which can be obtained by finding that x and y are ±4 and ±10, respectively.
This correct answer A
Step-by-step explanation:
The student is asking about the possible value of x + y given the equation x2 = 100y2 - 16.
To find the possible values of x and y, we can rewrite the equation as x2 + 16 = 100y2 where both sides of the equation can be seen as perfect squares. The left side becomes (x+4)(x-4), and the right side is (10y)2.
Therefore, we can conclude that x = ±4 and y = ±10. Adding x and y could give us 14, which is option A, since we can get x = +4 and y = +10 or x = -4 and y = -10.
This correct answer A. 14