8.1. Show that the following equations have no integer solutions. a. 423-Туз-2003
mod use Show that the following equations have no integer solutions: (4) 25 + 12x2 + 24x + 1 = 0.
Show that the following equations have no integer solutions: (4) 25 + 12x2 + 24x + 1 = 0. (1) x4 + x + 1 = 0; (2) 12x + 5 = y2; (3) x? +6x +1 = 0;
Show that the following equations have no integer solutions: (4) 25 + 12x2 + 24x + 1 = 0. (1) x4 + x + 1 = 0; (2) 12x + 5 = y2; (3) x? +6x +1 = 0;
3) Show that the set of al numbers that are solutions of polynomial equations with integer coefficients is a countable set.
Number Theory 8.29) Use descent to prove that x3 + 2y3 (0,0,0) 423 has no integer solutions other than
4) Show that the set of all numbers that are not solutions of polynomial equations with integer coefficients is an uncountable set. Hint: Show that if A is uncountable, B is countable and A- BUC then C is uncountable.
Rational Expressions and Equations Find all real solutions. Be sure to check for extraneous solutions. Show all work and steps. 3y-1/ y^2 + 1 = 1 y = 1, 2
Show that solutions to Maxwell’s equations (for E⃗ and B⃗ ) satisfy the wave equation, thus predicting that the solutions (EM waves) are in fact traveling waves.With what speed do the waves travel?
c) For what values of 2. does the following set of equations have non trivial solutions for x. y. -(1+1)x + y + 3a = 0 x+(2-2)y=0 3x +(2-2)==0
DIFFERENTIAL EQUATIONS Solutions of Systems of Linear Differential Equations (L01.5 - 15 points) Show that the general solution of the nonhomogeneous linear system is x=(1 71}x+ []}<+[4.]e + 3' X=al_2-vzlevat +al-1 + vale-vēt + [1]{2+{2}]++ [4]