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If x + y = 10 and xy = 21, what is the value of x^2 + y^2? (2021)

Practice Questions

Q1
If x + y = 10 and xy = 21, what is the value of x^2 + y^2? (2021)
  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 x^2 + y^2? (2021)
  • Step 1: Start with the equations given: x + y = 10 and xy = 21.
  • Step 2: Recall the formula for x^2 + y^2, which is x^2 + y^2 = (x + y)^2 - 2xy.
  • Step 3: Substitute the value of x + y into the formula: (10)^2.
  • Step 4: Calculate (10)^2, which equals 100.
  • Step 5: Now substitute the value of xy into the formula: 2(21).
  • Step 6: Calculate 2(21), which equals 42.
  • Step 7: Now, subtract the result from Step 6 from the result from Step 4: 100 - 42.
  • Step 8: Calculate 100 - 42, which equals 58.
  • Step 9: Therefore, the value of x^2 + y^2 is 58.
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