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3x² – 11x + 10 = 0
4y² + 24y + 35 = 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 'A'. Can you explain this answer?
Verified Answer
3x² – 11x + 10 = 04y² + 24y + 35 = 0a)X > Yb)X <...
3x² – 11x + 10 = 0
x = 1.6, 2
4y² + 24y + 35 = 0
y = – 2.5, -3.5
x = 1.6, 2
4y² + 24y + 35 = 0
y = – 2.5, -3.5
Most Upvoted Answer
3x² – 11x + 10 = 04y² + 24y + 35 = 0a)X > Yb)X <...
Understanding the Equations
The equations provided are:
1. 3x² – 11x + 10 = 0
2. 4y² + 24y + 35 = 0
We'll solve these equations to find the values of x and y.
Solving for x
To find x, we can use the quadratic formula:
- a = 3, b = -11, c = 10
Discriminant (D) = b² - 4ac = (-11)² - 4(3)(10) = 121 - 120 = 1
Since D > 0, there are two real distinct roots:
- x₁ = [11 + √1] / 6 = 12 / 6 = 2
- x₂ = [11 - √1] / 6 = 10 / 6 ≈ 1.67
Thus, x can take values of approximately 1.67 and 2.
Solving for y
For y, we use the quadratic formula:
- a = 4, b = 24, c = 35
Discriminant (D) = b² - 4ac = (24)² - 4(4)(35) = 576 - 560 = 16
Since D > 0, there are also two real distinct roots:
- y₁ = [-24 + √16] / 8 = -20 / 8 = -2.5
- y₂ = [-24 - √16] / 8 = -28 / 8 = -3.5
Thus, y can take values of approximately -2.5 and -3.5.
Comparing x and y
Now we compare the values of x and y:
- x (1.67, 2) are both greater than y (approximately -3.5, -2.5).
Conclusion
Since both values of x are greater than both values of y, we can conclude:
- The correct answer is option 'A': X > Y.
The equations provided are:
1. 3x² – 11x + 10 = 0
2. 4y² + 24y + 35 = 0
We'll solve these equations to find the values of x and y.
Solving for x
To find x, we can use the quadratic formula:
- a = 3, b = -11, c = 10
Discriminant (D) = b² - 4ac = (-11)² - 4(3)(10) = 121 - 120 = 1
Since D > 0, there are two real distinct roots:
- x₁ = [11 + √1] / 6 = 12 / 6 = 2
- x₂ = [11 - √1] / 6 = 10 / 6 ≈ 1.67
Thus, x can take values of approximately 1.67 and 2.
Solving for y
For y, we use the quadratic formula:
- a = 4, b = 24, c = 35
Discriminant (D) = b² - 4ac = (24)² - 4(4)(35) = 576 - 560 = 16
Since D > 0, there are also two real distinct roots:
- y₁ = [-24 + √16] / 8 = -20 / 8 = -2.5
- y₂ = [-24 - √16] / 8 = -28 / 8 = -3.5
Thus, y can take values of approximately -2.5 and -3.5.
Comparing x and y
Now we compare the values of x and y:
- x (1.67, 2) are both greater than y (approximately -3.5, -2.5).
Conclusion
Since both values of x are greater than both values of y, we can conclude:
- The correct answer is option 'A': X > Y.
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Community Answer
3x² – 11x + 10 = 04y² + 24y + 35 = 0a)X > Yb)X <...
3x² – 11x + 10 = 0
x = 1.6, 2
4y² + 24y + 35 = 0
y = – 2.5, -3.5
x = 1.6, 2
4y² + 24y + 35 = 0
y = – 2.5, -3.5
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3x² – 11x + 10 = 04y² + 24y + 35 = 0a)X > Yb)X < Yc)X ≥ Yd)X ≤ Ye)X = Y or relation cannot be establishedCorrect answer is option 'A'. Can you explain this answer?
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