What is x, if `x^(3)=1.5^(3)-0.9^(3)-2.43`

Options

A. `-0.5`
B. `0.6`
C. `-0.7`
D. `-1.6`

Answer

To solve the equation \( x^3 = 1.5^3 - 0.9^3 - 2.43 \), we will follow these steps:

### Step 1: Calculate \( 1.5^3 \)
First, we need to find the value of \( 1.5^3 \).
\[ 1.5^3 = 1.5 \times 1.5 \times 1.5 = 3.375 \]

### Step 2: Calculate \( 0.9^3 \)
Next, we find the value of \( 0.9^3 \).
\[ 0.9^3 = 0.9 \times 0.9 \times 0.9 = 0.729 \]

### Step 3: Substitute the values into the equation
Now we substitute the calculated values back into the equation:
\[ x^3 = 3.375 - 0.729 - 2.43 \]

### Step 4: Perform the subtraction
Now we perform the subtraction step by step:
1. First, calculate \( 3.375 - 0.729 \):
\[ 3.375 - 0.729 = 2.646 \]
2. Then, subtract \( 2.43 \) from \( 2.646 \):
\[ 2.646 - 2.43 = 0.216 \]

### Step 5: Set up the final equation
Now we have:
\[ x^3 = 0.216 \]

### Step 6: Solve for \( x \)
To find \( x \), we take the cube root of both sides:
\[ x = \sqrt[3]{0.216} \]

### Step 7: Calculate the cube root
Now we calculate the cube root:
\[ x = 0.6 \]

### Final Answer
Thus, the value of \( x \) is:
\[ \boxed{0.6} \]

---