Please Solve:
x + (sqrt11-x) = 5
A. 2
B. 7
C. 2, 7
D. No solution
Note that the x's cancel out. What does that leave you with? Can the resulting equation ever be true?
Please be very cautious when you transcribe an equation to post, because the presence and placement of parentheses are critical. Incorrect answers will be provided if the question is not posted correctly.
x + (sqrt11-x) = 5
is probably to be interpreted as:
x + sqrt(11-x) = 5
As Mr. Bob mentioned, the answer depends on whether the square-root value can be interpreted as ± or simply +. This is a "nuance" of the question which can be interpreted by the student, namely whether the course content expect the square-root to be interpreted as ±.
x + sqrt(11-x) = 5
sqrt(11-x) = (5-x)
11-x = (5-x)² = 25-10x+x²
x² - 9x + 14 = 0
(x-7)(x-2) = 0
x=2 or 7.
Since we squared at one point, the values should be back-substituted to verify the answer.
2+sqrt(11-x)=2+sqrt(9)=2+3=5 OK
7+sqrt(11-7)=7+sqrt(4)=7+2=9 incorrect
7-sqrt(11-7)=7-sqrt(4)=7-2=5 OK, but -sqrt required.
So A, B and C correspond to acceptance of +sqrt(), -sqrt() or ±sqrt() for your answer. Your course notes will most probably give you more hints.
See also:
http://www.jiskha.com/display.cgi?id=1249251936
I say there is no solution, but Mr. Bob told me that 2,7 are solutions? What is correct here?
2,7 are mathematically correct solutions, as explained by Mr. Bob.
(D) is definitely incorrect.
To solve the equation x + (sqrt(11) - x) = 5, we can follow these steps:
1. Start by simplifying the equation. Combine the 'x' terms on the left side of the equation:
x + sqrt(11) - x = 5
The 'x' terms cancel each other out:
sqrt(11) = 5
2. Next, isolate the square root term on one side of the equation. Subtracting 5 from both sides gives:
sqrt(11) - 5 = 0
3. To isolate the square root, square both sides of the equation:
(sqrt(11) - 5)^2 = 0^2
11 - 10sqrt(11) + 25 = 0
4. Combine like terms:
-10sqrt(11) + 36 = 0
5. Solve for 'sqrt(11)' by subtracting 36 from both sides:
-10sqrt(11) = -36
6. Divide both sides by -10 to solve for 'sqrt(11)':
sqrt(11) = 36/10
sqrt(11) = 3.6
7. Now, we substitute the value of 'sqrt(11)' back into the original equation and solve for 'x':
x + (sqrt(11) - x) = 5
Plug in the value of 'sqrt(11)':
x + (3.6 - x) = 5
Simplify the equation:
x + 3.6 - x = 5
3.6 = 5
The equation is not true. Since the last step leads to a contradiction (3.6 = 5), there is no solution to the equation.
Therefore, the correct answer is D. No solution.