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

It's time for board exam results to be declared and students are both anxious and excited to know how well they fared. Now, let's add equations and 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 + b^2 = 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. 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. Find the quadratic equation, whose roots are and ChatGPT's solution: The quadratic equation with roots and can be written in the form: )) = 0 Expanding the left-hand side of this equation using the distributive property, we get: x^2 - x - x + = 0 Simplifying this expression, we get: x^2 - 4x + 1 = 0 Therefore, the quadratic equation whose roots are and is: x^2 - 4x + 1 = 0 For this problem, though the answer is correct, the method used by ChatGPT is not suitable. Let's now check one last problem and see how ChatGPT responds to it: 5. tan ϴ= 5/12, find the value of / ChatGPT's solution: We can start by using the identities: sin ϴ = tan ϴ cos ϴ cos 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 = = ) Substituting the value of sin ϴ from the above equation, we get: sin ϴ = )) sin ϴ = 5/13 cos ϴ = √ = √) = 12/13 Now, we can substitute the values of sin ϴ and cos ϴ in the expression: / / 17/13 / = -17/7 Therefore, the value of / is -17/7 In this case as well, ChatGPT opted for a very long procedure to solve the problem.