document.write( "Question 588770: If $\"+sqrt+%28x%5E2+-5x+-11%29+%2B+13+=x+\"$ , then what value is $\"x%5E2-3x%2B3\"$ ? \n" ); document.write( "

Algebra.Com's Answer #374676 by KMST(5328) $\"\"$ $\"About$

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Something is wrong with the problem, or my interpretation.
\n" ); document.write( "I cannot find a real x that is a solution of that equation.
\n" ); document.write( "If there is no x, how could there be an $\"x%5E2-3x%2B3\"$ ?
\n" ); document.write( "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,
\n" ); document.write( "then $\"+x%5E2+-5x+-11%3E=0\"$ and $\"x%3E=13\"$ .
\n" ); document.write( "Then, squaring both sides, we get
\n" ); document.write( " $\"x%5E2+-5x+-11=%28x-13%29%5E2+\"$ --> $\"x%5E2+-5x+-11=x%5E2-26x%2B169\"$ --> $\"-5x-11=-26x%2B169\"$ --> $\"-5x-11%2B26x%2B11=-26x%2B169%2B26x%2B11\"$ --> $\"21x=180\"$ --> $\"x=180%2F21\"$ --> $\"x=60%2F7\"$
\n" ); document.write( "But that is only a solution of $\"x%5E2+-5x+-11=%28x-13%29%5E2+\"$
\n" ); document.write( "It is not a solution of $\"+sqrt+%28x%5E2+-5x+-11%29+%2B+13+=x+\"$ <--> $\"+sqrt+%28x%5E2+-5x+-11%29=x-13+\"$
\n" ); document.write( "because it makes $\"x-13%3C0\"$ \n" ); document.write( "

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