Kumpulan Artikel Kecerdasan Buatan

Matematika: Wolfram Alpha, Bing, Bard, dan ChatGPT

Yogyakarta, Rabu, 31 Mei 2023

Djoko Luknanto: Di WhatsApp Group, beberapa minggu yang lalu, ada yang posting teka-teki matematika. Sederhana sebenarnya, 1 + 1/(1 + 1/x) = 834/420, tetapi saya malas menghitung, karena sudah jelas tinggal melakukan manipulasi aljabar langsung. Saya gunakan web Wolfram Alpha untuk menghitung, tentu saja langsung ketemu jawabannya secara akurat, karena memang Wolfram Alpha dirancang untuk itu; yaitu x = 69.

Aljabar sederhana menghasilkan:

1+1/(1+1/x)=834/420
  1/(1+1/x)=834/420-1
  1/(1+1/x)=(834-420)/420
  1/(1+1/x)=414/420
      1+1/x=420/414
        1/x=420/414-1
        1/x=(420-414)/414
        1/x=6/414
          x=414/6
          x=69

Kemudian saya coba menghitung menggunakan ChatGPT, Google Bard AI, serta Microsoft Bing AI Copilot. Ternyata semuanya salah! Mengapa menghitung matematika sederhana kecerdasan buatan membuat kesalahan. Saya cermati baris per baris jawaban ketiganya, ternyata masing-masing menggunakan cara yang berbeda, namun salah semua jawabannya!

Jawaban ketiganya saya sertakan di bawah ini.

1. Yang paling mengherankan adalah jawab Microsoft Bing AI, karena hanya salin-rekat dari jawaban situs lain, yang ternyata salah melakukan intrepretasi inputnya. Jawabannya sama sekali salah!
2. Untuk jawaban Google Bard AI dan ChatGPT, harus dicermati satu per satu, karena jawaban menyertakan hitungan satu persatu, namun ada kesalahan pada rincian jawabannya.
3. Oleh karena itu kuncinya memang kita harus memandu kecerdasan buatan untuk mendapatkan jawaban yang benar. Pada saat rincian jawaban ada yang keliru, kita dapat memberikan masukan agar jawaban dihitung kembali.

Wolfram Alpha: Jawaban Wolfram Alpha dapat dilakukan dengan klik langsung di sini, atau lihat di bawah ini:

Gambar 1. Jawaban dari Wolfram Alpha untuk persamaan di atas.

Microsoft Bing AI Copilot versi Windows Professional 11: That's a tricky equation!

According to Symbolab, a step-by-step calculator for math problems², the solution is:

You can see the detailed steps and explanations on how to solve it by clicking on this link: ²

I hope that helps!

Source: Conversation with Bing, 5/31/2023
(1) Step-by-Step Calculator - Symbolab. https://www.symbolab.com/solver.
(2) Mathway | Algebra Problem Solver. https://www.mathway.com/algebra.
(3) Solve for x Calculator - Mathway. https://www.mathway.com/Calculator/solve-for-x-calculator.

Microsoft Bing AI Copilot versi Android: The solution to the equation 1+1/(1+1/x)=834/420 is x = 6. You can solve it by following these steps:

1. Subtract 1 from both sides of the equation to get 1/(1+1/x) = 414/420.
2. Take the reciprocal of both sides of the equation to get 1+1/x = 420/414.
3. Subtract 1 from both sides of the equation to get 1/x = (420/414)-1.
4. Simplify the right side of the equation to get 1/x = 6/207.
5. Take the reciprocal of both sides of the equation to get x = 207/6.

I hope that helps! Let me know if you have any other questions.

Source: Conversation with Bing, 5/31/2023
(1) Mathway | Algebra Problem Solver. https://www.mathway.com/algebra.
(2) Step-by-Step Calculator - Symbolab. https://www.symbolab.com/solver.
(3) Solve 1/x-1-1/x+1 | Microsoft Math Solver. https://mathsolver.microsoft.com/en/solve-problem/

Catatan Djoko Luknanto: Baris ke 4 seharusnya 1/x = 6/414, setelah diberi tahu Bing melakukan koreksi di bawah ini.

The correct solution to the equation 1+1/(1+1/x)=834/420 is x = 414/6 = 69. You can solve it by following these steps:

1. Subtract 1 from both sides of the equation to get 1/(1+1/x) = 414/420.
2. Take the reciprocal of both sides of the equation to get 1+1/x = 420/414.
3. Subtract 1 from both sides of the equation to get 1/x = (420/414)-1.
4. Simplify the right side of the equation to get 1/x = 6/414.
5. Take the reciprocal of both sides of the equation to get x = 414/6.

I hope that helps! Let me know if you have any other questions.

Google Bard AI: Sure, I can help you with that.

To solve for x, we can first cross-multiply the equation to get:

(1+1/(1+1/x)) * x = 834/420

Catatan Djoko Luknanto: Ini jelas keliru karena ruas kanan tidak dikalikan x.

This simplifies to:

x^2 + x - 834/420 = 0

We can then use the quadratic formula to solve for x:

x = (-1 ± v(1^2 - 4 * 1 * (-834/420))) / (2 * 1)
x = (-1 ± v(1 + 3336/420)) / 2
x = (-1 ± v(3756/420)) / 2
x = (-1 ± v(19 * 196/420)) / 2
x = (-1 ± 19/21) / 2
x = (-1/2 ± 19/21)
x = 10/21 or -11/21

Since x cannot be negative, we can conclude that x = 10/21.

Therefore, the value of x that satisfies the equation 1+1/(1+1/x)=834/420 is 10/21.

ChatGPT: To solve the equation 1 + 1/(1 + 1/x) = 834/420, we can start by simplifying the expression on the left side of the equation.

Let's find a common denominator for the fractions on the left side of the equation. The denominator for the fraction 1/x can be multiplied by (1 + 1/x) to get a common denominator of x.

 1 + 1/(1 + 1/x) = 1 + (x/(x + 1)) / x
                 = 1 + (x/(x + 1)) * (1/x)
                 = 1 + (x/x(x + 1))
                 = 1 + (1/(x + 1))

Catatan Djoko Luknanto: Ini jelas keliru, perhatikan baris pertama seharusnya ruas kanan adalah 1 + (x/(1 + 1/x)) / x.

Now the equation becomes:

1 + 1/(x + 1) = 834/420

Next, we can subtract 1 from both sides of the equation:

1/(x + 1) = 834/420 - 1
          = 834/420 - 420/420
          = (834 - 420)/420
          = 414/420

To get rid of the fraction, we can cross-multiply:

1 * 420 = (x + 1) * 414
420 = 414x + 414
420 - 414 = 414x
6 = 414x

Finally, we can solve for x by dividing both sides by 414:

6/414 = x/1
1/69 = x

Therefore, the solution to the equation 1 + 1/(1 + 1/x) = 834/420 is x = 1/69.