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If x + y = 10 and xy = 21, what is the value of x² + y²?

Practice Questions

Q1
If x + y = 10 and xy = 21, what is the value of x² + y²?
  1. 49
  2. 59
  3. 61
  4. 41

Questions & Step-by-Step Solutions

If x + y = 10 and xy = 21, what is the value of x² + y²?
  • Step 1: Start with the equations given: x + y = 10 and xy = 21.
  • Step 2: We need to find the value of x² + y².
  • Step 3: Use the formula x² + y² = (x + y)² - 2xy.
  • Step 4: Substitute the value of x + y into the formula: (10)².
  • Step 5: Calculate (10)², which is 100.
  • Step 6: Now substitute the value of xy into the formula: 2 * 21.
  • Step 7: Calculate 2 * 21, which is 42.
  • Step 8: Now, subtract 42 from 100: 100 - 42.
  • Step 9: Calculate 100 - 42, which gives you 58.
  • Step 10: Therefore, the value of x² + y² is 58.
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