Question

If 3^x +2^y = 985 and 3^x −2^y = 473, what is the value of xy?

Answer 1

Answer: 48.

Step-by-step explanation: Given that 3^x + 2^y = 985 …(1), and

3^x - 2^y = 473 …(2).

Add (1) and (2) to get

2*3^x = 1458, or

3^x = 729 = 3^6

Hence x = 6.

From (1) 2^y =985 =729 = 256 = 2^8, or y = 8.

Therefore xy = 6*8 = 48.

Answer 2

Answer:

Given that 3^x + 2^y = 985 …(1), and

3^x - 2^y = 473 …(2).

Add (1) and (2) to get

2 X 3^x = 1458, or

3^x = 729 = 3^6

Hence x = 6.

From (1) 2^y =985 =729 = 256 = 2^8, or y = 8.

Therefore xy = 6 X 8 = 48.

hope it help u