# solutions

1. ### Find integer solutions

Find integer solutions of system: x + y = z arctan x = arctan y + arctan z
2. ### Need help to verify the number of solutions

Given equation x^2 +x +\lambda =0 \; ,x\in \mathbb{R}. Verify N - the number of solutions, using any software (matlab, calculators... etc.) N_{\lambda } =\frac{\displaystyle 1 + \lim_{s\rightarrow \infty} \left[-2\left(1+e^{-2s(-1-4\lambda)}\right)+1\right]}{2}\lim_{s\rightarrow \infty}...
3. ### Number of solutions

Express the number of solutions of equation(EQ) in terms of \lambda. (EQ) x^2 +x +\lambda =0 \; ,x\in \mathbb{R}.
4. ### How many solutions does the differential equation have?

The Initial Value Problem yâ€²=y^2/3, y(0)=0 has ? (a) No solution. (b) Unique solution. (c) Two solutions. (d) Infinitely many solutions. As I understood, one solution is y=0 itself and other solution comes on solving the differential equation as 3y^(1/3)= x+c, on putting the initial...
5. ### Number of solutions of transcendental equation

Find how many solutions the equation has ? x^2 -2x =(-1)^x \; , x\in \mathbb{Z}.
6. ### Number of solutions

(eq1) F(x)=0 ; (eq2) F(x/2)=0 . If (eq1) has two solutions , how many solutions are for (eq2) ?
7. ### Number of solutions

Given equation(with respect to x): x^n +x=nx , how many real solutions the equation has ? x\geq 0 \; and n\in \mathbb{N} .
8. ### Number of Integral solutions

if |x-2| -|x+1| =p has exactly one solution then the no. of integral values of p is

A ladder AB, which is set up with B on the horizontal ground and A against a vertical wall, makes an angle of 71Â° with the ground. It is prevented from slipping by a tight rope PQ of length 1.68 meters, fixed at P to the foot of the wall and at Q to the ladder, |AB|. Calculate, in centimetres...
10. ### Number of integer solutions..

How many integer solutions does this expression have: x1*x2*3*x4 = 770 So, 2*5*7*11 = 770 But the catch is that either one, two, or three of these variables can be 1 as well. So, 70*11*1*1 = 770 Similarly, 770*1*1*1 = 770. The way I proceeded with this question, was a follows: i) No "1"...
11. ### Help me with the complete solutions please.

https://docs.google.com/document/d/1NbN_cfLaftkvy9UEeOkeHe-hMs3daJ98VOnDdBIzax4/edit?usp=drivesdk Questions are attached in the pic and also in the link above.
12. ### Rational Solutions of the tan function in the context of a video game

First of all, I'd like to note that I believe I've already solved the problem I'm about to pose (it just comes down to there being just two rational solutions to the tan function) and as such, am not really in need of help with it. I'm only posting this as a log of a "real-world" application to...
13. ### Number of solutions

Find the number of pairs (n_1,n_2) that satisfies the equation below: n_1 + n_2 = x\; \; where n_1 ,n_2 ,x \in \mathbb{N}
14. ### Where can I find the previous yearâ€™s IIT JAM mathematics papers with solutions?

Hello If you are preparing for IIT JAM Mathematics, you should solve previous year question papers. It will help you to prepare better. The benefit of solving the exam papers are: After solving the previous year papers, you have an idea about paper level. You will know the weightage...
15. ### Stuck on finding solutions

How do I factor z^5 - 3z^4 - 16z + 48 = 0? I was thinking rational root theorem. But when I look at the solution it uses three back to back iterations of synthetic division, and I got slightly confused. Any tips?
16. ### How many solutions to the following equation

How to prove that tanx=10x has exactly 3 roots in the interval (-pi/2, pi/2)? I defined g(x) = tanx-10x. I think I should derive it and use Rolle's theorem and Intermediate value theorem. But I just can't figure out how exactly. Thanks
17. ### Infinite solutions problem

I am trying to solve following problem. I am trying to find x,y,z in terms of \lambda. And then equating the resultant equation to 0. Am I correct?
18. ### Polynomial solutions

I'm not able to define the solutions. How many solutions does the polynomial equation below have for n natural? Note: (without complex solutions). \sum_{j=1}^{j=n} x^j =x^n+x^{n-1}+...+x^2+x=0
19. ### How to prove the inequality of solutions for two Cauchy problems?

View image Thank you for your suggestion.
20. ### Algebraic Solutions

I didn't understand the meaning of the below sentences, if it means the coefficients/ solutions of an Algebraic equations only lies in Real numbers then it will not be true since we can have a polynomial of the below type with Complex coefficients and Complex solutions as well. If it does...