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If a + b = 5 and ab = 6, what is the value of a² + b²?

Practice Questions

Q1
If a + b = 5 and ab = 6, what is the value of a² + b²?
  1. 7
  2. 11
  3. 25
  4. 19

Questions & Step-by-Step Solutions

If a + b = 5 and ab = 6, what is the value of a² + b²?
  • Step 1: We are given two equations: a + b = 5 and ab = 6.
  • Step 2: We need to find the value of a² + b².
  • Step 3: We can use the formula a² + b² = (a + b)² - 2ab.
  • Step 4: Substitute the value of a + b into the formula: (5)².
  • Step 5: Calculate (5)², which is 25.
  • Step 6: Now substitute the value of ab into the formula: 2 * 6.
  • Step 7: Calculate 2 * 6, which is 12.
  • Step 8: Now we have a² + b² = 25 - 12.
  • Step 9: Calculate 25 - 12, which is 13.
  • Step 10: Therefore, the value of a² + b² is 13.
  • Algebraic Identities – Understanding the identity a² + b² = (a + b)² - 2ab to simplify expressions involving sums and products of variables.
  • Quadratic Relationships – Recognizing the relationship between the sum and product of two numbers and how they relate to their squares.
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