Question 10

Statement 1 - If $$x$$ is a real number such that $$\sqrt{x^2} = 4$$ then $$x = 4$$.<br>Statement 2 - If $$x$$ is a real number such that $$\sqrt{x^2} = 9$$ then $$x = \pm 3$$.

Solution

For real $$x$$, $$\sqrt{x^2} = |x|$$. From $$|x| = 4$$ we get $$x = \pm 4$$, so concluding $$x = 4$$ is wrong and Statement 1 is false. From $$|x| = 9$$ we get $$x = \pm 9$$, not $$\pm 3$$, so Statement 2 is also false.

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