Solve for x 3 square root of 2cos(x)+2=-1

Problem

3√(,2*cos(x)+2)=−1

Solution

1. Analyze the equation for possible solutions.

2. Observe the left side of the equation, which contains a principal square root multiplied by a positive constant.

3. Recall that the principal square root of any real number is non-negative by definition: √(,u)≥0

4. Determine that the product 3√(,2*cos(x)+2) must be greater than or equal to 0

5. Compare the left side to the right side, where −1<0

6. Conclude that there is no real value of x that satisfies the equation because a non-negative value cannot equal a negative value.

Final Answer

3√(,2*cos(x)+2)=−1⇒No real solution

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