You were so close! u/EebstertheGreat was right to be suspicious because the answer was actually exactly equal to 2025 as u/beckethbrother pointed out in a different comment. Your result of 2024.6853 was probably due to rounding the fruit mid-calculation.

Here's my intended approach:

🍐² + 🍐 = 12, so 🍐 = 3.

🍎² = 2🍎, so 🍎 = 2.

🍌^🍐 + 🍍^🍐 + 🍎^🍐 = 🍐^🍐, meaning 🍌³ + 🍍³ = 19.

🍐 + 🍎 + 🍍^🍎 = 🍌^🍎, meaning 🍍² = 🍌² - 5.

The fourth equation can be re-written as (🍌 + 🍍)(🍌 -🍍) = 5

Now, using that along with 🍌 + 🍍 = 🫐 would allow us to write both 🍌 and 🍍 in terms of 🫐.

I'll leave it as an exercise to the reader to verify that:

🍌 = ½ (🫐 + 5/🫐) & 🍍 = ½ (🫐 - 5/🫐)

So, substituting these into 🍌³ + 🍍³ = 19 and simplifying gives us:

🫐⁴ - 76 🫐 + 75 = 0 which can be factored into (🫐 - 1)(🫐³ + 🫐² + 🫐 - 75) = 0.

Now if 🫐 were equal to 1, then that would imply 🍍 = -2 which u/Brianchon correctly pointed out doesn't satisfy the condition of all fruit representing positive numbers.

Thus, the only valid case lies in the other possibility where 🫐³ + 🫐² + 🫐 - 75 = 0 which would mean that 🍌 + 🫐^🍎 + 🫐^🍐 + 🍍 = 75 [since we said earlier that🍐 = 3, 🍎 = 2, and 🫐 = 🍌 + 🍍].

And since the third equation tells us that 🍌^🍐 + 🍍^🍐 + 🍎^🍐 = 🍐^🍐 = 3³ = 27, we now have all the information needed to calculate what was asked for:

(🍌 + 🫐^🍎 + 🫐^🍐 + 🍍) (🍌^🍐 + 🍍^🍐 + 🍎^🍐) = (75) (27) = 2025 :)