Respuesta :
Yes, is it possible. Since the product of two negative numbers is a positive numbers, for any real number x you have
[tex] x \cdot x = x^2,\text{ but also }\ (-x)(-x) = x^2 [/tex]
So, a number and its opposite give the same result when squared. For example, both 3 and -3 give 9 when squared.
So, when a variable is squared into an equation, you will have two different solutions. For example, in the equation
[tex] x^2 = 25 [/tex]
You are looking for a number that gives 25 when squared. We know that 5 gives 25 when squared, but because of everything we said at the beginning, -5 also gives 25 when squared. So, the two solutions are 5 and -5.
About the last question, I assume that by "an equation with a squared variable" you mean a quadratic equation, i.e. something like
[tex] ax^2+bx+c=0 [/tex]
In this case, there can be two different solutions, one double solution, or no solution at all. In fact, the solving formula involves a square root, namely
[tex] \sqrt{b^2-4ac} [/tex]
and a root doesn't always exist.
