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What is the value of x in the equation x2 + 9 = 6x ?
- a)x =1 or x = 3
- b)x = 1 only
- c)x = -1 or x = -3
- d)x = 3 only
- e)No real value of x
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
What is the value of x in the equation x2 + 9 = 6x ?a)x =1 or x = 3b)x...
- Given, x2 + 9 = 6x
- ⇒ x2 - 6x + 9 = 0
- ⇒ x2 -3x -3x + 9 = 0
- ⇒ x ( x - 3) - 3 ( x - 3) = 0
- Taking (x-3) common from the equation , we get
- ⇒ (x - 3) (x - 3) = 0
- ⇒ x = 3
Most Upvoted Answer
What is the value of x in the equation x2 + 9 = 6x ?a)x =1 or x = 3b)x...
Understanding the Equation
To solve the equation x² + 9 = 6x, we first need to rearrange it into standard quadratic form.
- Move all terms to one side:
x² - 6x + 9 = 0
Factoring the Quadratic
Now, we can factor the quadratic equation:
- Recognize that x² - 6x + 9 can be factored as:
(x - 3)(x - 3) = 0
or
(x - 3)² = 0
Finding the Solutions
To find the value of x, set the factor equal to zero:
- Solve for x:
x - 3 = 0
Therefore,
x = 3
Analyzing the Options
Now let’s compare this solution with the provided options:
- a) x = 1 or x = 3
- b) x = 1 only
- c) x = -1 or x = -3
- d) x = 3 only
- e) No real value of x
Only option d) x = 3 only is correct since the equation yields a single solution.
Conclusion
Thus, the correct answer is option 'D', confirming that x = 3 is the only real value satisfying the equation.
To solve the equation x² + 9 = 6x, we first need to rearrange it into standard quadratic form.
- Move all terms to one side:
x² - 6x + 9 = 0
Factoring the Quadratic
Now, we can factor the quadratic equation:
- Recognize that x² - 6x + 9 can be factored as:
(x - 3)(x - 3) = 0
or
(x - 3)² = 0
Finding the Solutions
To find the value of x, set the factor equal to zero:
- Solve for x:
x - 3 = 0
Therefore,
x = 3
Analyzing the Options
Now let’s compare this solution with the provided options:
- a) x = 1 or x = 3
- b) x = 1 only
- c) x = -1 or x = -3
- d) x = 3 only
- e) No real value of x
Only option d) x = 3 only is correct since the equation yields a single solution.
Conclusion
Thus, the correct answer is option 'D', confirming that x = 3 is the only real value satisfying the equation.
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Question Description
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