Please Solve:

Question

x + (sqrt11-x) = 5

A. 2
B. 7
C. 2, 7
D. No solution

Answer 1

Note that the x's cancel out. What does that leave you with? Can the resulting equation ever be true?

Answer 2

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

Answer 3

I say there is no solution, but Mr. Bob told me that 2,7 are solutions? What is correct here?

Answer 4

2,7 are mathematically correct solutions, as explained by Mr. Bob.

(D) is definitely incorrect.