document.write( "Question 1060987: Q.1 If $\"+%28x%2Biy%29%5E%281%2F3%29=a%2Bib+\"$ then show that $\"+4%28a%5E2+-+b%5E2%29=x%2Fa+%2B+y%2Fb+\"$ \r
\n" ); document.write( "\n" ); document.write( "Q.2 Find the real no.s x and y if $\"+%28x-iy%29%283%2B5i%29+\"$ is the conjugate of $\"+-6-24i+\"$ . \n" ); document.write( "

Algebra.Com's Answer #675803 by KMST(5328) $\"\"$ $\"About$

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Q.1 $\"%28x%2Biy%29%5E%28%221+%2F+3%22%29=a%2Bib\"$ <---> $\"x%2Biy=%28a%2Bib%29%5E3\"$
\n" ); document.write( " $\"x%2Biy=%28a%2Bib%29%5E3\"$
\n" ); document.write( " $\"x%2Biy=a%5E3%2B3a%5E2%2A%28ib%29%2B3a%2A%28ib%29%5E2%2B%28ib%29%5E3\"$
\n" ); document.write( " $\"x%2Biy=a%5E3%2B3ba%5E2%2Ai%2B3a%2A%28-b%5E2%29-b%5E3%2Ai\"$
\n" ); document.write( " $\"x%2Biy=%28a%5E3-3ab%5E2%29%2B%283ba%5E2-b%5E3%29%2Ai\"$
\n" ); document.write( " $\"x%2Biy=a%28a%5E2-3b%5E2%29%2Bb%283a%5E2-b%5E2%29%2Ai\"$ ---> $\"system%28x=a%28a%5E2-3b%5E2%29%2Cy=b%283a%5E2-b%5E2%29%29\"$ ---> $\"system%28x%2Fa=a%5E2-3b%5E2%2Cy%2Fb=3a%5E2-b%5E2%29%29\"$
\n" ); document.write( "So,
\n" ); document.write( " $\"x%2Fa%2By%2Fb=a%5E2-3b%5E2%2B3a%5E2-b%5E2\"$
\n" ); document.write( " $\"x%2Fa%2By%2Fb=4a%5E2-4b%5E2\"$
\n" ); document.write( " $\"x%2Fa%2By%2Fb=4%28a%5E2-b%5E2%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Q.2 $\"%28x-iy%29%283%2B5i%29=3x%2B5x%2Ai-3y%2Ai%2B5y=%283x%2B5y%29%2B%285x-3y%29%2Ai\"$
\n" ); document.write( "The conjugate of $\"-6-24i\"$ is $\"-6%2B24i\"$ .
\n" ); document.write( " $\"%283x%2B5y%29%2B%285x-3y%29%2Ai=-6%2B24i\"$ --> $\"system%283x%2B5y=-6%2C5x-3y=24%29\"$ --> $\"highlight%28system%28x=3%2Cy=-3%29%29\"$
\n" ); document.write( "There are many ways to solve the system. For example,
\n" ); document.write( "we could start by multiplying the first equation times ( $\"-6\"$ , the second equation times $\"3\"$ and adding them to get
\n" ); document.write( " $\"-15x-25y%2B15x-9y=30%2B72\"$ --> $\"-34y=102\"$ --> $\"y=102%2F%28-34%29\"$ --> $\"y=-3%29\"$ .
\n" ); document.write( "Then, substituting $\"-3\"$ for $\"x\"$ in $\"3x%2B5y=-6\"$ , we get
\n" ); document.write( " $\"3x%2B5%28-3%29=-6\"$ --> $\"3x-15=-6\"$ --> $\"3x=15-6\"$ --> $\"3x=9\"$ --> $\"x=9%2F3\"$ --> $\"x=3\"$ . \n" ); document.write( "

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