SOLUTION: If {{{ sqrt (x^2 -5x -11) + 13 =x }}}, then what value is {{{x^2-3x+3}}} ?

Algebra ->  Equations -> SOLUTION: If {{{ sqrt (x^2 -5x -11) + 13 =x }}}, then what value is {{{x^2-3x+3}}} ?      Log On


   

Question 588770: If +sqrt+%28x%5E2+-5x+-11%29+%2B+13+=x+, then what value is x%5E2-3x%2B3 ?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Something is wrong with the problem, or my interpretation.
I cannot find a real x that is a solution of that equation.
If there is no x, how could there be an x%5E2-3x%2B3 ?
If +sqrt+%28x%5E2+-5x+-11%29+%2B+13+=x+ <--> +sqrt+%28x%5E2+-5x+-11%29=x-13+ and we are working in the real numbers,
then +x%5E2+-5x+-11%3E=0 and x%3E=13.
Then, squaring both sides, we get
x%5E2+-5x+-11=%28x-13%29%5E2+ --> x%5E2+-5x+-11=x%5E2-26x%2B169 --> -5x-11=-26x%2B169 --> -5x-11%2B26x%2B11=-26x%2B169%2B26x%2B11 --> 21x=180 --> x=180%2F21 --> x=60%2F7
But that is only a solution of x%5E2+-5x+-11=%28x-13%29%5E2+
It is not a solution of +sqrt+%28x%5E2+-5x+-11%29+%2B+13+=x+ <--> +sqrt+%28x%5E2+-5x+-11%29=x-13+
because it makes x-13%3C0