Question

If (a,b) = \(a^2+b^2\) and g(a, b) = \(\frac{2}{b^2}\) \([a^2+b^2]\), then what is the value of f(6,3)-g(8,4)?

• A. 30
• B. 35
• C. 40
• D. 45
• E. 40

Answer 1

The Correct Option is B

To solve the problem, we need to find the value of \( f(6, 3) - g(8, 4) \) where: 

The function \( f(a, b) = a^2 + b^2 \), and

The function \( g(a, b) = \frac{2}{b^2} \times [a^2 + b^2] \).

We will calculate each step by step:

1. Find \( f(6, 3) \):
   • Using \( f(a, b) = a^2 + b^2 \), substitute \( a = 6 \) and \( b = 3 \).
   • \( f(6, 3) = 6^2 + 3^2 \).
   • \( f(6, 3) = 36 + 9 = 45 \).
2. Find \( g(8, 4) \):
   • Using \( g(a, b) = \frac{2}{b^2} \times [a^2 + b^2] \), substitute \( a = 8 \) and \( b = 4 \).
   • First calculate \( a^2 + b^2 \):
   • \( 8^2 + 4^2 = 64 + 16 = 80 \).
   • Now calculate \( g(8, 4) \):
   • \( g(8, 4) = \frac{2}{4^2} \times 80 \).
   • \( g(8, 4) = \frac{2}{16} \times 80 \).
   • \( g(8, 4) = \frac{1}{8} \times 80 = 10 \).
3. Calculate \( f(6, 3) - g(8, 4) \):
   • Substitute the values found in steps 1 and 2:
   • \( f(6, 3) - g(8, 4) = 45 - 10 \).
   • \( f(6, 3) - g(8, 4) = 35 \).

The value of \( f(6, 3) - g(8, 4) \) is 35.

Conclusion: The correct answer is 35.