12 − x9 = 11 true or false,

Question

x = -9

Answer 1

To determine if the statement \( 12 - x^9 = 11 \) is true when \( x = -9 \), we can substitute \( x = -9 \) into the equation:

1. Substitute \( x = -9 \) into the equation:

   \[ 12 - (-9)^9 = 11 \]

2. Calculate \( (-9)^9 \):

   Since \(-9\) raised to an odd exponent is negative, we have:

   \[ (-9)^9 = -387420489 \]

3. Substitute that value back into the equation:

   \[ 12 - (-387420489) = 11 \]

   This simplifies to:

   \[ 12 + 387420489 = 11 \]

   Which simplifies to:

   \[ 387420501 = 11 \]

Since \( 387420501 \neq 11 \), the statement is false.

Answer 2

So what is the correct answer

Answer 3

To find the correct value of \( x \) for the equation \( 12 - x^9 = 11 \), let's solve it step by step:

1. Start with the original equation: \[ 12 - x^9 = 11 \]

2. Subtract 12 from both sides to isolate \( -x^9 \): \[ -x^9 = 11 - 12 \] \[ -x^9 = -1 \]

3. Multiply both sides by -1: \[ x^9 = 1 \]

4. To solve for \( x \), take the ninth root of both sides. The ninth root of 1 can be: \[ x = 1 \] or any complex roots of unity, but for real-valued solutions, the principal root is: \[ x = 1 \]

Thus, the correct answer is: \[ x = 1 \]