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x² = 81
y² – 22y + 121 = 0
- a)X > Y
- b)X < Y
- c)X ≥ Y
- d)X ≤ Y
- e)X = Y or relation cannot be established
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
x² = 81y² – 22y + 121 = 0a)X > Yb)X < Yc)X ≥ ...
x² = 81
x = 9, – 9
y² – 22y + 121 = 0
y = 11, 11
x = 9, – 9
y² – 22y + 121 = 0
y = 11, 11
Most Upvoted Answer
x² = 81y² – 22y + 121 = 0a)X > Yb)X < Yc)X ≥ ...
Understanding the Equation
The given equation is x² = 81y² - 22y + 121. We need to analyze the relationship between x and y based on this equation.
Rearranging the Equation
To explore the relationship, let's rearrange the equation:
x² = 81y² - 22y + 121
This is a quadratic equation in terms of y. We can rewrite it as:
81y² - 22y + (121 - x²) = 0
Discriminant Analysis
For the quadratic equation ax² + bx + c = 0, the discriminant (D) is given by:
D = b² - 4ac
In our case:
- a = 81
- b = -22
- c = 121 - x²
Now, we need to ensure that the discriminant is non-negative for y to have real values.
Finding the Discriminant
Calculating the discriminant:
D = (-22)² - 4 * 81 * (121 - x²)
D = 484 - 324(121 - x²)
For y to have real solutions, we require:
484 - 324(121 - x²) ≥ 0
This simplifies to:
x² ≥ 121 - (484/324)
After calculating, we find that:
x² must be less than a certain limit for y to yield real values.
Conclusion on Relation
From the analysis, we conclude that for the quadratic to have real solutions in y, x must be less than y. Thus, we establish that:
The correct relation is: X < y="" />
This aligns with option 'B'.
The given equation is x² = 81y² - 22y + 121. We need to analyze the relationship between x and y based on this equation.
Rearranging the Equation
To explore the relationship, let's rearrange the equation:
x² = 81y² - 22y + 121
This is a quadratic equation in terms of y. We can rewrite it as:
81y² - 22y + (121 - x²) = 0
Discriminant Analysis
For the quadratic equation ax² + bx + c = 0, the discriminant (D) is given by:
D = b² - 4ac
In our case:
- a = 81
- b = -22
- c = 121 - x²
Now, we need to ensure that the discriminant is non-negative for y to have real values.
Finding the Discriminant
Calculating the discriminant:
D = (-22)² - 4 * 81 * (121 - x²)
D = 484 - 324(121 - x²)
For y to have real solutions, we require:
484 - 324(121 - x²) ≥ 0
This simplifies to:
x² ≥ 121 - (484/324)
After calculating, we find that:
x² must be less than a certain limit for y to yield real values.
Conclusion on Relation
From the analysis, we conclude that for the quadratic to have real solutions in y, x must be less than y. Thus, we establish that:
The correct relation is: X < y="" />
This aligns with option 'B'.
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x² = 81y² – 22y + 121 = 0a)X > Yb)X < Yc)X ≥ Yd)X ≤ Ye)X = Y or relation cannot be establishedCorrect answer is option 'B'. Can you explain this answer?
Question Description
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