1 1 vote The number of integer solutions of equation $2|x|\left(x^{2}+1\right)=5 x^{2}$ is Quantitative Aptitude cat2023-set1 quantitative-aptitude number-systems + – admin 5.3k points 1.5k views answer comment Share Follow Print See all 2 Comments 2 2 Comments reply rhl 642 points commented Jul 4, 2025 i edited by rhl Jul 4, 2025 reply Follow flag not an ideal way to do but i just started putting values starting from $0$ then $1,2,3....$ clearly i was able to see $0,2,-2$ are the solution satisfying the equation. Another way is to simply just forget about the mod and open the brackets. (but do keep in mind its presence) $2x^3+2x=5x^2$ solving this equation we will get $x=0,2,\frac{1}{2}$ since $0.5$ is not an integer we can ignore it. so $|x| = 0,2$ therefore $x=0,2,-2$ 1 1 replyShare Ninja004 490 points commented Jul 4, 2025 reply Follow flag We can see that the function is an even function so the graph will be symmetric about the vertical axis, hence we can simply put x in place of |x| and solve for all the positive solutions and then we can be sure that there will be solutions on the negative x axis as well just of the negative magnitude. One more way to think about it from functions pov 1 1 replyShare Please log in or register to add a comment.
