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Recently I have been solving a electrostatics questions where you are given two charges and want to find where the third charge should be kept so that net force on it is 0. It generates a quadratic equations which can be solved and correct answer could be choosed intuitively. But when I saw its solution, the quadratic was solved by taking square root both sides.

My question is how can we exactly know where we can take square root both side to solve a quadratic and where we can't?

swarnim
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    If we know that both sides are non-negative, we are allowed to take the square root and we are also allowed to square both sides. – Peter Jun 03 '22 at 12:09
  • In which way is your question connected to [tag:linear-algebra]? – José Carlos Santos Jun 03 '22 at 12:14
  • @Peter What I am asking is when I used to solve quadratic in maths class, I was told not to take square root both sides because we might lost one of the answers but in the physics question I explained above, quadratic has been solved by taking square root both sides. I wanna know how are we so sure that we will not lose the right answer? – swarnim Jun 03 '22 at 12:18
  • @JoséCarlosSantos sorry it's my fault i have removed that tag – swarnim Jun 03 '22 at 12:19
  • Could you tag the question you refer to? – insipidintegrator Jun 03 '22 at 12:31
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    In physics there is often extra information that can be deduced from the assumption that the problem is physically realizable. For example, the mass of a particle is never negative. It might be helpful if you showed the actual problem and the solution with the square root. Remember to use MathJax for the formulas: http://math.stackexchange.com/help/notation – David K Jun 03 '22 at 13:15

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You can always take the square root on both sides as long as the terms are nonnegative, e.g. $$ x^2=4\ \Rightarrow \ \sqrt{x^2} =\sqrt 4.$$ What you can not do is claim that $\sqrt{x^2}=x$, since $x$ may be negative!

Ruy
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