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If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

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Question: If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

Options:

  1. 49
  2. 59
  3. 61
  4. 41

Correct Answer: 49

Solution: 

Using the identity a^2 + b^2 = (a + b)^2 - 2ab, we get a^2 + b^2 = 10^2 - 2*21 = 100 - 42 = 58.

If a + b = 10 and ab = 21, what is the value of a^2 + b^2?

Practice Questions

Q1
If a + b = 10 and ab = 21, what is the value of a^2 + b^2?
  1. 49
  2. 59
  3. 61
  4. 41

Questions & Step-by-Step Solutions

If a + b = 10 and ab = 21, what is the value of a^2 + b^2?
  • Step 1: Identify the given equations: a + b = 10 and ab = 21.
  • Step 2: Recall the identity for a^2 + b^2: a^2 + b^2 = (a + b)^2 - 2ab.
  • Step 3: Substitute the value of a + b into the identity: (a + b)^2 = 10^2.
  • Step 4: Calculate 10^2: 10^2 = 100.
  • Step 5: Substitute the value of ab into the identity: 2ab = 2 * 21.
  • Step 6: Calculate 2 * 21: 2 * 21 = 42.
  • Step 7: Now substitute these values into the identity: a^2 + b^2 = 100 - 42.
  • Step 8: Calculate 100 - 42: 100 - 42 = 58.
  • Step 9: Therefore, the value of a^2 + b^2 is 58.
  • Algebraic Identities – Understanding and applying the identity a^2 + b^2 = (a + b)^2 - 2ab to find the sum of squares of two variables.
  • Systems of Equations – Using given equations to derive new relationships between variables.
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