If `3x^(2) = 10 ^(2) - 5 ^(2)` find the value of x? (a) 7 (b) 5 (c) 9 (d) 11

Options

A. 7
B. 5
C. 9
D. 11

Answer

To solve the equation \( 3x^2 = 10^2 - 5^2 \), we can follow these steps:

### Step 1: Calculate \( 10^2 \) and \( 5^2 \)
First, we need to find the squares of 10 and 5.
\[ 10^2 = 100 \]
\[ 5^2 = 25 \]

### Step 2: Substitute the values into the equation
Now, substitute these values back into the equation:
\[ 3x^2 = 100 - 25 \]

### Step 3: Simplify the right side
Next, simplify the right side of the equation:
\[ 3x^2 = 75 \]

### Step 4: Divide both sides by 3
To isolate \( x^2 \), divide both sides of the equation by 3:
\[ x^2 = \frac{75}{3} = 25 \]

### Step 5: Take the square root of both sides
Now, take the square root of both sides to find \( x \):
\[ x = \sqrt{25} = 5 \]

### Conclusion
Thus, the value of \( x \) is \( 5 \).

### Answer
The correct option is (b) 5.

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