document.write( "Question 173565: Given that (alpha) is the root of the equation x^2= 2x-1, show that:
\n" ); document.write( "(a) (alpha)^3= 3(alpha) -2 ,\r
\n" ); document.write( "\n" ); document.write( "(b) (alpha)^4-(alpha)^2= 2(alpha)-2 \n" ); document.write( "

Algebra.Com's Answer #128450 by solver91311(24713) $\"\"$ $\"About$

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$\"x%5E2=2x-1\"$ → $\"x%5E2-2x%2B1=0\"$ → $\"%28x-1%29%5E2=0\"$ → $\"x=1\"$ , therefore $\"alpha=1\"$ \r
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\n" ); document.write( "\n" ); document.write( "(a) $\"alpha%5E3=1%5E3=1\"$ and $\"3%2Aalpha+-+2+=+3%2A1+-+2+=+1\"$ \r
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\n" ); document.write( "\n" ); document.write( "(b) $\"alpha%5E4-alpha%5E2=1%5E4-1%5E2=1-1=0\"$ and $\"2%2Aalpha+-+2=+2%2A1-2=+0\"$ \r
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