Discussion

Explanation:

Let 3^x = a and 5^y = b

⇒ 3^x + 5^y = 52
⇒ a + b = 52

Also, 3^2x-2 + 5^y+1 = 206
⇒ 3^2x/9 + 5 × 5^y = 206
⇒ 3^2x + 45 × 5^y = 1854
⇒ a² + 45b = 1854   ...(2)

(2) - 45 × (1)

⇒ a² - 45a = 1854 - 2340
⇒ a² - 45a + 486 = 0
⇒ (a - 18)(a - 27) = 0
⇒ a = 18 or 27

⇒ 3^x = 18 or 27​​​​​​​
Since x is an integer, 3^x = 27 and x = 3.

Also, b = 5^y = 52 - 27 = 25, hence, y = 2

∴ x + y = 3 + 2 = 5.

Hence, option (c).

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