Archimedes Laboratory Project™
Puzzles & Mental Activities that Enhance Critical and Creative Thinking Skills

	Some clever people say that there is no real solution to this equation. Is it correct? If not, please, explain... Existe-t-il une solution réelle à cette équation? Si oui, expliquez… Esiste una soluzione reale a questa equazione? Se sì, diteci come… You can comment and discuss this puzzle on our FaceBook web page. › Click to show/hide the solution Solution: As the numerators of the fractions are the same, we can equate the denominators, so: x2 + x + 4 = 2x2 + x + 5 we get x2 + 1 = 0, which has NO real solutions. Sure, the rule: "if 2 fractions are equal and their numerators are equal, then their denominators are equal" is correct but sometimes it is necessary to specify "if 2 fractions are equal and their numerators are equal AND NOT ZERO…". Thus considering the possibility that the numerator may be zero we can find 2 real solutions just by equating the denominators as follows: x2 – 2x – 3 = 0 With x = 3 and -1 Please spread the word about the Sunday Puzzle!

Text and images by Gianni A. Sarcone 
Labels: SUNDAY PUZZLE, puzzles to solve, recreational mathematics, real solution
You can use the material shown on this page for educational purpose only as long as you credit us [© G. Sarcone, www.archimedes-lab.org] and link back to archimedes-lab.org
Sunday Puzzle by Gianni A. Sarcone is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Based on a work at http://www.archimedes-lab.org.

Archimedes' Lab exists thanks to sponsorised ads and online sales of puzzle products and activities.