@Sze Ting Chen shouldn't x_1 + x_2 = 2m/(m^2 + 1) according to question? You have written 2m/(m^2 - 1) which doesn't match the question. Same thing goes with the product of roots.

@Sze Ting Chen can you please tell me why you didn't solve (x_1 - x_2) and from where those +- sign came. Can you also give a detailed and proper answer?

We derive the +- sign from the normal quadratic equation (as my teacher used it to solve the problem), and I'll try to give a more detailed explanation of the answer. Now that I see some of the mistakes my teacher made, I'll do the question again and find a more comprehensive answer.

Bro

Ans is in between of [0,4]

is it right??

No. You need to express (x_1)^3 - (x_2)^3 in terms of the other variable m

This is the full answer to the question (I arrived at the same answer):

I used a way too long winded strategy that involved getting rid of and adding more square roots (hence why I used my teacher's strategy to post here)

@Sze Ting Chen shouldn't x_1 + x_2 = 2m/(m^2 + 1) according to question? You have written 2m/(m^2 - 1) which doesn't match the question. Same thing goes with the product of roots.

@Sze Ting Chen can you please tell me why you didn't solve (x_1 - x_2) and from where those +- sign came. Can you also give a detailed and proper answer?

We derive the +- sign from the normal quadratic equation (as my teacher used it to solve the problem), and I'll try to give a more detailed explanation of the answer. Now that I see some of the mistakes my teacher made, I'll do the question again and find a more comprehensive answer.