If x and y are positive integers, and 4x^2=3y, then which of the follo
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03 Jun 2022, 20:38
Stepping back and looking at the equation and what it implies:
(Number value on left side) must equal (number value on right side)
Which means, the values on each side must have the same Prime Factorization, given that X and Y must be positive integers.
4 * (x)^2 = 3 * y
Since 4 is NOT divisible by 3, the other term on the LEFT side (i.e., (x)^2) MUST be divisible by 3 in order for the condition of X and Y as a positive integer to remain true.
The MINIMUM value we must make X is 3
Inserting 3 in for X:
4 (3)^2 = 3 * y
Divide each side of the equation by 3
4 * 3 = y
Therefore, the MINIMUM value of Y must be 12 (which makes sense since the coefficient 3 on the right side is not divisible by 4)
Minimum values:
x = 3
y = 12
(X)^2 = (3)^2 = 9
(Y)^2 = (12)^2 = 144
XY = 3 * 12 = 36
At the MINIMUM Possible values of (x, y) in order for the equation to be satisfied and the variables to be positive integers, all three terms MUST be divisible by 9
E: I, II, and III
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