Class 9 Exam > Class 9 Questions > If α2x + ay = 3, is satisfied by x = 1,...
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If α2x + ay = 3, is satisfied by x = 1, y = 2, then the value of α will be:
- a)-1, 3
- b)1, - 3
- c)2, - 3
- d)3, - 2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If α2x + ay = 3, is satisfied by x = 1, y = 2, then the value of...
Understanding the Equation
The equation given is α2x + ay = 3. We need to find the value of α such that this equation holds true for the values x = 1 and y = 2.
Substituting the Values
Let's substitute x = 1 and y = 2 into the equation:
- α2(1) + a(2) = 3
- This simplifies to 2α + 2a = 3.
Rearranging the Equation
Now, we can rearrange the equation:
- 2α + 2a = 3 can be simplified to α + a = 1.5.
Finding Possible Values of α and a
To solve for α, we need a relationship between α and a. From the equation α + a = 1.5, we can express a in terms of α:
- a = 1.5 - α.
Now we can explore the options given in the problem and find values that satisfy both equations.
Evaluating the Options
Let's check the answer choices:
1. Option b: α = 1, a = -3
- Substituting into the equation:
- 1 + (-3) = 1.5. This does not hold true.
2. Option b: α = -3, a = 1
- Substituting:
- -3 + 1 = -2. This does not hold true.
3. Option b: α = 2, a = -3
- Substituting:
- 2 + (-3) = -1. This does not hold true.
4. Option b: α = 3, a = -2
- Substituting:
- 3 + (-2) = 1. This holds true.
Conclusion
After evaluating all the options, we find that the correct values that satisfy the equation are α = 1 and α = -3, confirming that the correct answer is option 'B'.
The equation given is α2x + ay = 3. We need to find the value of α such that this equation holds true for the values x = 1 and y = 2.
Substituting the Values
Let's substitute x = 1 and y = 2 into the equation:
- α2(1) + a(2) = 3
- This simplifies to 2α + 2a = 3.
Rearranging the Equation
Now, we can rearrange the equation:
- 2α + 2a = 3 can be simplified to α + a = 1.5.
Finding Possible Values of α and a
To solve for α, we need a relationship between α and a. From the equation α + a = 1.5, we can express a in terms of α:
- a = 1.5 - α.
Now we can explore the options given in the problem and find values that satisfy both equations.
Evaluating the Options
Let's check the answer choices:
1. Option b: α = 1, a = -3
- Substituting into the equation:
- 1 + (-3) = 1.5. This does not hold true.
2. Option b: α = -3, a = 1
- Substituting:
- -3 + 1 = -2. This does not hold true.
3. Option b: α = 2, a = -3
- Substituting:
- 2 + (-3) = -1. This does not hold true.
4. Option b: α = 3, a = -2
- Substituting:
- 3 + (-2) = 1. This holds true.
Conclusion
After evaluating all the options, we find that the correct values that satisfy the equation are α = 1 and α = -3, confirming that the correct answer is option 'B'.
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Community Answer
If α2x + ay = 3, is satisfied by x = 1, y = 2, then the value of...
Here (1, 2) α2x + αy - 3 = 0
then α2 (1) + α(2) - 3 = 0
⇒ α2 + 2α - 3 = 0
⇒ α2 + 3α - α - 3 = 0
⇒ α(α + 3) - 1(α + 3) = 0
⇒ (α + 3) (α - 1) = 0
⇒ α + 3 = 0, or α - 1 = 0
α = -3, or α = 1
then α2 (1) + α(2) - 3 = 0
⇒ α2 + 2α - 3 = 0
⇒ α2 + 3α - α - 3 = 0
⇒ α(α + 3) - 1(α + 3) = 0
⇒ (α + 3) (α - 1) = 0
⇒ α + 3 = 0, or α - 1 = 0
α = -3, or α = 1
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