Question

If (3^x + 4^y = 12), prove that (x + y = xy).

a) (x + y = xy)
b) (x + y ≠ xy)
c) Insufficient information to prove
d) None of the above

Answer 1

There is insufficient information to prove that (x + y = xy) for all values of x and y satisfying the equation 3^x + 4^y = 12, as no direct relationship is given that links x and y in this manner.

Step-by-step explanation:

The given equation is 3^x + 4^y = 12, and we are asked to evaluate whether (x + y = xy) based on this. Without any further restrictions or additional information about the relationship between x and y, we cannot definitively solve for x and y such that both x + y and xy are equal. We can consider specific integer values for x and y that satisfy 3^x + 4^y = 12, but these do not lead to a general proof that x + y is equal to xy in all possible cases. For instance, if x = 1 and y = 1, the equation becomes 3^1 + 4^1 = 3 + 4 which equals 7, not 12. This leads us to conclude that there is insufficient information to prove that (x + y = xy) holds true for all x and y that satisfy the given equation.