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I. 2X² – 15√2X + 56 = 0
II. 2Y² – 17√2Y + 72= 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. 2X² – 15√2X + 56 = 0II. 2Y² – 17√...
X = 7/√2, 8/√2
Y = 8/√2, 9/√2
Y = 8/√2, 9/√2
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I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√...
Understanding the Equations
We have two quadratic equations to analyze:
- I. 2X² – 15√2X + 56 = 0
- II. 2Y² – 17√2Y + 72 = 0
Step 1: Solving for X
To find the roots (X values) of equation I:
- The coefficients are: a = 2, b = -15√2, c = 56.
- Using the quadratic formula, X = [ -b ± √(b² - 4ac) ] / 2a.
Calculating the discriminant (b² - 4ac):
- b² = (-15√2)² = 450
- 4ac = 4 * 2 * 56 = 448
- Discriminant = 450 - 448 = 2 (positive, hence two real roots)
Now, compute the roots:
- X1 = [15√2 + √2] / 4 = (15 + 1)√2 / 4 = 16√2 / 4 = 4√2
- X2 = [15√2 - √2] / 4 = (15 - 1)√2 / 4 = 14√2 / 4 = 3.5√2
Step 2: Solving for Y
Now for equation II:
- The coefficients are: a = 2, b = -17√2, c = 72.
- Using the quadratic formula again.
Calculating the discriminant:
- b² = (-17√2)² = 578
- 4ac = 4 * 2 * 72 = 576
- Discriminant = 578 - 576 = 2 (positive, two real roots)
Now, compute the roots:
- Y1 = [17√2 + √2] / 4 = (17 + 1)√2 / 4 = 18√2 / 4 = 4.5√2
- Y2 = [17√2 - √2] / 4 = (17 - 1)√2 / 4 = 16√2 / 4 = 4√2
Comparing X and Y
From the calculations:
- X values: 4√2 and 3.5√2
- Y values: 4.5√2 and 4√2
Conclusion
- The maximum value of X (4√2) is equal to the minimum value of Y (4√2).
- Since the values of X can be less than or equal to Y, the correct answer is option 'D': X ≤ Y.
We have two quadratic equations to analyze:
- I. 2X² – 15√2X + 56 = 0
- II. 2Y² – 17√2Y + 72 = 0
Step 1: Solving for X
To find the roots (X values) of equation I:
- The coefficients are: a = 2, b = -15√2, c = 56.
- Using the quadratic formula, X = [ -b ± √(b² - 4ac) ] / 2a.
Calculating the discriminant (b² - 4ac):
- b² = (-15√2)² = 450
- 4ac = 4 * 2 * 56 = 448
- Discriminant = 450 - 448 = 2 (positive, hence two real roots)
Now, compute the roots:
- X1 = [15√2 + √2] / 4 = (15 + 1)√2 / 4 = 16√2 / 4 = 4√2
- X2 = [15√2 - √2] / 4 = (15 - 1)√2 / 4 = 14√2 / 4 = 3.5√2
Step 2: Solving for Y
Now for equation II:
- The coefficients are: a = 2, b = -17√2, c = 72.
- Using the quadratic formula again.
Calculating the discriminant:
- b² = (-17√2)² = 578
- 4ac = 4 * 2 * 72 = 576
- Discriminant = 578 - 576 = 2 (positive, two real roots)
Now, compute the roots:
- Y1 = [17√2 + √2] / 4 = (17 + 1)√2 / 4 = 18√2 / 4 = 4.5√2
- Y2 = [17√2 - √2] / 4 = (17 - 1)√2 / 4 = 16√2 / 4 = 4√2
Comparing X and Y
From the calculations:
- X values: 4√2 and 3.5√2
- Y values: 4.5√2 and 4√2
Conclusion
- The maximum value of X (4√2) is equal to the minimum value of Y (4√2).
- Since the values of X can be less than or equal to Y, the correct answer is option 'D': X ≤ Y.
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I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√2Y + 72= 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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I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√2Y + 72= 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? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√2Y + 72= 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? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√2Y + 72= 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?.
I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√2Y + 72= 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? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√2Y + 72= 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? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√2Y + 72= 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?.
Solutions for I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√2Y + 72= 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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I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√2Y + 72= 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?, a detailed solution for I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√2Y + 72= 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? has been provided alongside types of I. 2X² – 15√2X + 56 = 0II. 2Y² – 17√2Y + 72= 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? theory, EduRev gives you an
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