Should Students Use ChatGPT To Solve Maths Problems? Let's Find Out

We tried solving problems using ChatGPT and found out that although it gave the correct answers for the problems, the process used by the chatbot was unnecessarily lengthy.

It's time for board exam results to be declared and students are both anxious and excited to know how well they fared. When preparations were at their peak, many students might have leveraged OpenAI's surprisingly capable chatbot — ChatGPT — for various tasks, which can range from completing assignments to solving maths problems. We decided to put ChatGPT's famed skills to the test and used it to solve some 2023 CBSE Class 10 math problems of WX1YZ/5 Series, Set 1, and the results were quite interesting, to say the least. 

We tried solving five problems using ChatGPT, comprising trigonometry, basic arithmetic, and algebra. It was found out that although ChatGPT gave the correct answers, the process used by it for some problems was extremely lengthy and it included some unnecessary steps. So, now the question arises — should students use ChatGPT for solving math problems?

Let's consider the first problem:

1. Point P(x,y) is equidistant from points A(5, 1) and B(1, 5), Prove that x=y 

ChatGPT's solution:

Let's use the distance formula to find the distance between point P(x,y) and points A(5,1) and B(1,5): 

Distance between P and A: 

d(P, A) = √[(x - 5)^2 + (y - 1)^2] 

Distance between P and B: 

d(P, B) = √[(x - 1)^2 + (y - 5)^2] 

We are given that point P is equidistant from points A and B. This means that: 

d(P, A) = d(P, B) 

Substituting the distances we calculated above, we get: 

√[(x - 5)^2 + (y - 1)^2] = √[(x - 1)^2 + (y - 5)^2] 

Squaring both sides, we get: 

(x - 5)^2 + (y - 1)^2 = (x - 1)^2 + (y - 5)^2 

Expanding both sides, we get: 

x^2 - 10x + 25 + y^2 - 2y + 1 = x^2 - 2x + 1 + y^2 - 10y + 25 

Simplifying and cancelling out like terms, we get: 

-8x + 8y = 0 

Dividing both sides by 8, we get: 

x - y = 0 

Therefore, x = y, which proves that if point P(x,y) is equidistant from points A(5,1) and B(1,5), then x = y. 

This was a 2-mark question in the paper and such a long process of solving it is unnecessary. This problem can be solved directly by using the midpoint formula.

By finding the midpoint of A and B, it will be seen that the value of x and y are the same, which in turn proves that x=y.

Let's try another problem, and see what ChatGPT answers:

2.  If a cosϴ + b sinϴ= m and a sinϴ- b cosϴ=n, then prove that a^2 + b^2= m^2 + n^2

ChatGPT's solution:

We will start by squaring the given equations:
(a cosϴ + b sinϴ)^2 = m^2
(a sinϴ - b cosϴ)^2 = n^2

Expanding the squares, we get:
a^2 cos^2ϴ + 2ab cosϴ sinϴ + b^2 sin^2ϴ = m^2 ...(1)
a^2 sin^2ϴ - 2ab cosϴ sinϴ + b^2 cos^2ϴ = n^2 ...(2)

Now, let's add equations (1) and (2) to eliminate the cross-term:
a^2 cos^2ϴ + 2ab cosϴ sinϴ + b^2 sin^2ϴ + a^2 sin^2ϴ - 2ab cosϴ sinϴ + b^2 cos^2ϴ = m^2 + n^2

Simplifying and cancelling out the cross-terms, we get:
a^2 (cos^2ϴ + sin^2ϴ) + b^2 (cos^2ϴ + sin^2ϴ) = m^2 + n^2

Using the identity cos^2ϴ + sin^2ϴ = 1, we get:
a^2 + b^2 = m^2 + n^2

Therefore, we have proved that if a cosϴ + b sinϴ = m and a sinϴ - b cosϴ = n, then a^2 + b^2 = 
m^2 + n^2

For this problem, ChatGPT solved correctly and also the method used is correct as well. Full marks! 

Let's check out a third problem and see what happens:

3. Using prime factorisation, find LCM and HCF of 96 and 120

ChatGPT's solution:

To find the LCM and HCF of 96 and 120 using prime factorization, we need to first factorize each number into its prime factors:
96 = 2^5 * 3 120 = 2^3 * 3 * 5

To find the HCF, we take the highest power of each common prime factor:
HCF = 2^3 * 3 = 24

To find the LCM, we take the highest power of each prime factor, including those that are not common, and multiply them together:
LCM = 2^5 * 3 * 5 = 960

Therefore, the HCF of 96 and 120 is 24, and the LCM is 960

For this problem too, ChatGPT solved this in the correct method, giving the right answer.

Let's head to the fourth question:

4. Find the quadratic equation, whose roots are (2+√3) and (2-√3)

ChatGPT's solution:

The quadratic equation with roots (2+√3) and (2-√3) can be written in the form:
(x - (2+√3))(x - (2-√3)) = 0

Expanding the left-hand side of this equation using the distributive property, we get:
x^2 - x(2+√3) - x(2-√3) + (2+√3)(2-√3) = 0

Simplifying this expression, we get:
x^2 - 4x + 1 = 0

Therefore, the quadratic equation whose roots are (2+√3) and (2-√3) is:
x^2 - 4x + 1 = 0

For this problem, though the answer is correct, the method used by ChatGPT is not suitable. There are direct formulas with the help of which the problem can be solved. Also, this was an MCQ question, so spending so much time on an MCQ is not required.

Let's now check one last problem and see how ChatGPT responds to it:

5. tan ϴ= 5/12, find the value of (sin ϴ+cosϴ)/ (sinϴ-cosϴ)

ChatGPT's solution:

We can start by using the identities:
sin ϴ = tan ϴ cos ϴ
cos ϴ = √(1 - sin^2 ϴ)
tan ϴ = sin ϴ / cos ϴ

Using the given value of tan ϴ = 5/12, we can find sin ϴ and cos ϴ as:
sin ϴ = (tan ϴ)(cos ϴ) = (5/12) (√(1 - sin^2 ϴ))

Substituting the value of sin ϴ from the above equation, we get:
sin ϴ = (5/12) (√(1 - (25/144)))
sin ϴ = 5/13
cos ϴ = √(1 - sin^2 ϴ) = √(1 - (25/169)) = 12/13

Now, we can substitute the values of sin ϴ and cos ϴ in the expression:
(sin ϴ + cos ϴ) / (sin ϴ - cos ϴ)
(5/13 + 12/13) / (5/13 - 12/13)
17/13 / (-7/13)
= -17/7

Therefore, the value of (sin ϴ + cos ϴ) / (sin ϴ - cos ϴ) is -17/7

In this case as well, ChatGPT opted for a very long procedure to solve the problem. Instead, this could be done in two to three steps, using a triangle and Pythagoras theorem or by using the relation tan ϴ = sin ϴ / cos ϴ.

Should Students Use ChatGPT? No!

So, after testing five problems, it could be noted that ChatGPT gave all correct answers but the method opted by the AI, in some cases, was rather long and unnecessary.

Although ChatGPT can give correct answers, students should not rely on it completely, as it is very important for them to learn the concepts and know the simpler methods of solving problems.

Also, in the case of students, AI or any such tools should not be used at all during the initial stages of concept building.

Lastly, if students are indeed using AI-driven tools to check their answers, it should be used under the supervision of their parents or teachers who can guide them with the correct method of problem-solving. 

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