If a^2 + b^2 = 50 and a \times b = 7, find \frac{a - b}{a + b} , where a \gt b \gt 0

  1. A. \frac{4}{3}
  2. B. \frac{3}{4} ✓
  3. C. \frac{3}{5}
  4. D. \frac{5}{3}

Correct Answer: B. \frac{3}{4}

Explanation

Using identities: (a+b)^2 = a^2+b^2+2ab = 50+14 = 64, so a+b=8. And (a-b)^2 = a^2+b^2-2ab = 50-14 = 36, so a-b=6. Thus, \frac{a-b}{a+b} = \frac{6}{8} = \frac{3}{4}.

Practice more AFCAT Mathematics questions