Question

If a² + b² = 234 and ab = 108 then find the value of {a + b}/{a -b}

• A. 10
• B. 5
• C. 8
• D. 4

Answer 1

Answer:

B. 5

Calculating (a + b)

• We are given a² + b² = 234 and ab = 108.

• Using the identity (a + b)² = a² + b² + 2ab:

  • Substitute the given values: (a + b)² = 234 + 2(108)

  • Perform multiplication: (a + b)² = 234 + 216

  • Add the terms: (a + b)² = 450

  • Take the square root of both sides: a + b = √450

  • To simplify √450, factorize 450: 450 = 225 × 2. Since 225 is 15², we have 450 = 15² × 2.

  • Thus, a + b = √(15² × 2) = 15√2.

Calculating (a - b)

• Using the identity (a - b)² = a² + b² - 2ab:

  • Substitute the given values: (a - b)² = 234 - 2(108)

  • Perform multiplication: (a - b)² = 234 - 216

  • Subtract the terms: (a - b)² = 18

  • Take the square root of both sides: a - b = √18

  • To simplify √18, factorize 18: 18 = 9 × 2. Since 9 is 3², we have 18 = 3² × 2.

  • Thus, a - b = √(3² × 2) = 3√2.

Finding the Value of (a + b) / (a - b)

• Now, substitute the calculated values of (a + b) and (a - b) into the required expression:

  • (a + b) / (a - b) = (15√2) / (3√2)

  • The common term √2 in the numerator and denominator cancels out.

  • Simplify the fraction: (a + b) / (a - b) = 15 / 3

  • Perform the division: (a + b) / (a - b) = 5.