Question

(a) for what values of t will the statement be true? select \all real numbers\ if applicable. (sqrt4{t^4}=t) the statement is true for ({ t | square }). part 2 of 2 (b) for what values of t will the statement be true? select \all real numbers\ if applicable. (sqrt4{t^4}=|t|)

Explanation:

Step1: Simplify the left-hand side

$\sqrt[4]{t^4} = |t|$

Step2: Analyze equality for (a)

Set $|t| = t$. This holds when $t \geq 0$.

Step3: Analyze equality for (b)

Set $|t| = |t|$. This is always true for all real $t$.

Answer:

(a) $\{ t \mid t \geq 0 \}$
(b) all real numbers