document.write( "Question 1109050: Given a+b=1, a^3+b^3=16.
\n" ); document.write( "a). Expand (a+b)^3
\n" ); document.write( "b). Find the value of a^2 +b^2 \n" ); document.write( "

Algebra.Com's Answer #724070 by KMST(5328) $\"\"$ $\"About$

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a). $\"%28a%2Bb%29%5E3=a%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3\"$
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\n" ); document.write( " $\"a%2Bb=1\"$ --> $\"system%28%28a%2Bb%29%5E3=1%2C%22and%22%2C+%28a%2Bb%29%5E2=1%29\"$
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\n" ); document.write( "Substituting into $\"%28a%2Bb%29%5E3=a%5E3%2B3a%5E2b%2B3ab%5E2%2Bb%5E3\"$ , we get
\n" ); document.write( " $\"1=16%2B3a%5E2b%2B3ab%5E2\"$
\n" ); document.write( " $\"-15=3a%5E2b%2B3ab%5E2\"$
\n" ); document.write( " $\"-15=3ab%28a%2Bb%29\"$
\n" ); document.write( " $\"-15=3ab\"$
\n" ); document.write( " $\"-15%2F3=ab\"$
\n" ); document.write( " $\"ab=-5\"$
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\n" ); document.write( " $\"a%5E2%2Bb%5E2%2B2ab=%28a%2Bb%29%5E2\"$
\n" ); document.write( "Substituting $\"%28a%2Bb%29%5E2=1%29\"$ and $\"ab=-5\"$ , we get
\n" ); document.write( " $\"a%5E2%2Bb%5E2%2B2%28-5%29=1\"$
\n" ); document.write( " $\"a%5E2%2Bb%5E2-10=1\"$
\n" ); document.write( " $\"a%5E2%2Bb%5E2=1%2B10\"$
\n" ); document.write( " $\"a%5E2%2Bb%5E2=11\"$
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\n" ); document.write( "NOTE: You could use $\"system%28a%2Bb=1%2Cab=-5%29\"$ to find
\n" ); document.write( "that $\"a\"$ and $\"b\"$ are $\"%281+%2B-+sqrt%2821%29%29%2F2\"$ ,
\n" ); document.write( "and then calculate $\"a%5E2%2Bb%5E2\"$ ,
\n" ); document.write( "but it is not fun. \n" ); document.write( "

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