Question

Which statement is NOT true?

Answer 1

If x² = 100, then x = 10  →  NOT true

Because If x² = 100, then x = ±10

Answer 2

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. $x^2=100$, if and only if $x=10\text{ or }x=-10$.

Let us solve for x by taking square root of both sides of our given equation.

$\sqrt{x^2}=\sqrt{100}$

$\sqrt{x^2}=\sqrt{10^2}$

$x=\pm 10$

$x=10\text{ or }x=-10$

Therefore, our given statement is true.

B. $x^2=100$, then $x=10$.

Upon taking square root we will get positive and negative 10, therefore, the given statement is false.

C. If $x=-10$, then  $x^2=100$

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 $x=10$, then  $x^2=100$

Upon squaring 10 we will get 100, therefore, the given statement is true as well.