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I.2X² – (4+√14)X +√56 = 0
II.10Y² – (18+5√14)Y + 9√14 =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 'C'. Can you explain this answer?
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Verified Answer
I.2X² – (4+√14)X +√56 = 0II.10Y² – (...
X = 2, √14/2
Y = 9/5, √14/2
Y = 9/5, √14/2
Most Upvoted Answer
I.2X² – (4+√14)X +√56 = 0II.10Y² – (...
Understanding the Equations
The given equations are quadratic equations in X and Y. We need to analyze each equation to determine the relationship between their roots.
Equation I: 2X² - (4 + √14)X + √56 = 0
- For this quadratic equation in X, we can find the roots using the quadratic formula:
X = [-(b) ± √(b² - 4ac)] / (2a)
Here, a = 2, b = -(4 + √14), and c = √56.
- The roots' relationship will depend on the discriminant (D):
D = b² - 4ac.
If D > 0, there are two distinct real roots; if D = 0, one real root; and if D < 0,="" no="" real="" />
Equation II: 10Y² - (18 + 5√14)Y + 9√14 = 0
- Similarly, for this quadratic in Y, use the quadratic formula:
Y = [-(b) ± √(b² - 4ac)] / (2a)
Here, a = 10, b = -(18 + 5√14), and c = 9√14.
- Again, compute the discriminant (D):
D = b² - 4ac, with the same implications for the roots.
Comparing the Roots
- Both equations represent parabolas, and their roots can be numerical values based on the discriminants.
- If we compute the discriminants and find them to be equal, or if they yield roots that are numerically the same, we can establish that X = Y.
- If the discriminants are positive but yield different values, we would need to compare the roots directly to ascertain if X > Y or X < />
Conclusion
Given that the correct answer is 'C', it implies that after analyzing the roots from both equations, they can be equal or cannot be distinctly separated. Thus, X can be greater than or equal to Y depending on the specific values computed from the equations.
The given equations are quadratic equations in X and Y. We need to analyze each equation to determine the relationship between their roots.
Equation I: 2X² - (4 + √14)X + √56 = 0
- For this quadratic equation in X, we can find the roots using the quadratic formula:
X = [-(b) ± √(b² - 4ac)] / (2a)
Here, a = 2, b = -(4 + √14), and c = √56.
- The roots' relationship will depend on the discriminant (D):
D = b² - 4ac.
If D > 0, there are two distinct real roots; if D = 0, one real root; and if D < 0,="" no="" real="" />
Equation II: 10Y² - (18 + 5√14)Y + 9√14 = 0
- Similarly, for this quadratic in Y, use the quadratic formula:
Y = [-(b) ± √(b² - 4ac)] / (2a)
Here, a = 10, b = -(18 + 5√14), and c = 9√14.
- Again, compute the discriminant (D):
D = b² - 4ac, with the same implications for the roots.
Comparing the Roots
- Both equations represent parabolas, and their roots can be numerical values based on the discriminants.
- If we compute the discriminants and find them to be equal, or if they yield roots that are numerically the same, we can establish that X = Y.
- If the discriminants are positive but yield different values, we would need to compare the roots directly to ascertain if X > Y or X < />
Conclusion
Given that the correct answer is 'C', it implies that after analyzing the roots from both equations, they can be equal or cannot be distinctly separated. Thus, X can be greater than or equal to Y depending on the specific values computed from the equations.
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I.2X² – (4+√14)X +√56 = 0II.10Y² – (18+5√14)Y + 9√14 =0a)X > Yb)X <Yc)X ≥ Yd)X ≤ Ye)X = Y or relationship cannot be establishedCorrect answer is option 'C'. Can you explain this answer?
Question Description
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