Answer:
Statement represented by option B is not a correct choice.
Step-by-step explanation:
We have been given 4 statements. We are asked to choose the statement that is not true.
A. [tex]x^2=100[/tex], if and only if [tex]x=10\text{ or }x=-10[/tex].
Let us solve for x by taking square root of both sides of our given equation.
[tex]\sqrt{x^2}=\sqrt{100}[/tex]
[tex]\sqrt{x^2}=\sqrt{10^2}[/tex]
[tex]x=\pm 10[/tex]
[tex]x=10\text{ or }x=-10[/tex]
Therefore, our given statement is true.
B. [tex]x^2=100[/tex], then [tex]x=10[/tex].
Upon taking square root we will get positive and negative 10, therefore, the given statement is false.
C. If [tex]x=-10[/tex], then [tex]x^2=100[/tex]
Since we know that square of a negative number is positive, therefore, square of negative 10 is 100 and the given statement is true.
D. If [tex]x=10[/tex], then [tex]x^2=100[/tex]
Upon squaring 10 we will get 100, therefore, the given statement is true as well.
