document.write( "Question 301676: Solve: (x^2 - 5x +5)^(x^2 - 9x +20) = 1 \n" ); document.write( "

Algebra.Com's Answer #216302 by Alan3354(69443) $\"\"$ $\"About$

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Solve: (x^2 - 5x +5)^(x^2 - 9x +20) = 1
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\n" ); document.write( "Either (x^2 - 5x +5) = 1 or -1, or
\n" ); document.write( "x^2 - 9x +20 = 0
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\n" ); document.write( "If (x^2 - 5x +5) = -1, then the exponent has to be an even integer.
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\n" ); document.write( "x^2 - 9x +20 = 0
\n" ); document.write( "(x-5)*(x-4) = 0
\n" ); document.write( "x = 5
\n" ); document.write( "x = 4
\n" ); document.write( "-------
\n" ); document.write( "(x^2 - 5x +5) = +1
\n" ); document.write( "x^2 - 5x + 4 = 0
\n" ); document.write( "x = 1
\n" ); document.write( "x = 4
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\n" ); document.write( "Try the -1
\n" ); document.write( "(x^2 - 5x +5) = -1
\n" ); document.write( "x^2 - 5x + 6 = 0
\n" ); document.write( "x = 2
\n" ); document.write( "x = 3
\n" ); document.write( "The x=2 will give an even exponent and is valid
\n" ); document.write( "The x=3 --> an even exponent too.
\n" ); document.write( "x = 2, 3, 4 or 5
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