Question

Is it possible for two different numbers, when squared, to give the same result? What does this result tell you about solving an equation when the variable is squared? How many solutions will an equation like this have? Will there always be the same number of solutions for any equation with a squared variable? Explain.

Answer 1

x=4

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Answer 2

Hello,

Let's assume x and y the 2 numbers.

x²=y²
x²-y²=0
(x-y)(x+y)=0
x=y or x=-y


When the variable is squared we introduce extra solutions :

we must verify if each solution is exact.

If then 2 numbers are differents, x=-y

Example: 5 and -5 ==> 5²=25 , (-5)²=25