Questions: Solve. √[4](k-3)+1=0

Solve. √[4](k-3)+1=0
Transcript text: Solve. \[ \sqrt[4]{k-3}+1=0 \]
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Solution

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Solution Steps

Hint

To solve the equation, isolate the fourth root on one side, then raise both sides to the fourth power to eliminate the root. Finally, solve for the variable by simplifying the resulting equation.

Step 1: Isolate the Fourth Root

Starting with the equation: \[ \sqrt[4]{k-3} + 1 = 0 \] we isolate the fourth root: \[ \sqrt[4]{k-3} = -1 \]

Step 2: Raise Both Sides to the Fourth Power

Next, we raise both sides to the fourth power to eliminate the root: \[ k - 3 = (-1)^4 \] This simplifies to: \[ k - 3 = 1 \]

Step 3: Solve for \( k \)

Now, we solve for \( k \) by adding 3 to both sides: \[ k = 1 + 3 \] Thus, we find: \[ k = 4 \]

Final Answer

\(\boxed{k = 4}\)

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