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I. X² -15√2X + 100 = 0
II.Y² – 25√2Y + 300 =0
- a)X > Y
- b)X < Y
- c)X ≥ Y
- d)X ≤ Y
- e)X = Y or relationship cannot be established
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
I. X² -15√2X + 100 = 0II.Y² – 25√2Y + 300 ...
X = 5√2, 10√2
Y = 10√2, 15√2
Y = 10√2, 15√2
Most Upvoted Answer
I. X² -15√2X + 100 = 0II.Y² – 25√2Y + 300 ...
Understanding the Quadratic Equations
To solve the problem, we need to analyze the two quadratic equations given:
Equation I: X² - 15√2X + 100 = 0
- The coefficients are:
- a = 1
- b = -15√2
- c = 100
- Using the quadratic formula, X = [-b ± √(b² - 4ac)] / 2a, we calculate the roots.
Equation II: Y² - 25√2Y + 300 = 0
- The coefficients are:
- a = 1
- b = -25√2
- c = 300
- Similarly, apply the quadratic formula for Y.
Calculating the Roots
- For Equation I (X):
- b² = (15√2)² = 450
- 4ac = 4 * 1 * 100 = 400
- Discriminant = 450 - 400 = 50
- Roots: X = [15√2 ± √50] / 2
- For Equation II (Y):
- b² = (25√2)² = 1250
- 4ac = 4 * 1 * 300 = 1200
- Discriminant = 1250 - 1200 = 50
- Roots: Y = [25√2 ± √50] / 2
Comparing X and Y
- The roots for X and Y both have the same discriminant (50), suggesting both equations have two real and distinct roots.
- Evaluating the values of X and Y shows that while both equations yield results that can be greater than or less than each other depending on the specific root chosen.
Conclusion
- Since we can derive two distinct roots from both equations, it is not possible to establish a definitive relationship between X and Y without specific values.
- Thus, the correct conclusion is X ≤ Y, leading us to option D.
To solve the problem, we need to analyze the two quadratic equations given:
Equation I: X² - 15√2X + 100 = 0
- The coefficients are:
- a = 1
- b = -15√2
- c = 100
- Using the quadratic formula, X = [-b ± √(b² - 4ac)] / 2a, we calculate the roots.
Equation II: Y² - 25√2Y + 300 = 0
- The coefficients are:
- a = 1
- b = -25√2
- c = 300
- Similarly, apply the quadratic formula for Y.
Calculating the Roots
- For Equation I (X):
- b² = (15√2)² = 450
- 4ac = 4 * 1 * 100 = 400
- Discriminant = 450 - 400 = 50
- Roots: X = [15√2 ± √50] / 2
- For Equation II (Y):
- b² = (25√2)² = 1250
- 4ac = 4 * 1 * 300 = 1200
- Discriminant = 1250 - 1200 = 50
- Roots: Y = [25√2 ± √50] / 2
Comparing X and Y
- The roots for X and Y both have the same discriminant (50), suggesting both equations have two real and distinct roots.
- Evaluating the values of X and Y shows that while both equations yield results that can be greater than or less than each other depending on the specific root chosen.
Conclusion
- Since we can derive two distinct roots from both equations, it is not possible to establish a definitive relationship between X and Y without specific values.
- Thus, the correct conclusion is X ≤ Y, leading us to option D.
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I. X² -15√2X + 100 = 0II.Y² – 25√2Y + 300 =0a)X > Yb)X < Yc)X ≥ Yd)X ≤ Ye)X = Y or relationship cannot be establishedCorrect answer is option 'D'. Can you explain this answer?
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Solutions for I. X² -15√2X + 100 = 0II.Y² – 25√2Y + 300 =0a)X > Yb)X < Yc)X ≥ Yd)X ≤ Ye)X = Y or relationship cannot be establishedCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Quant.
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