document.write( "Question 1113675: Solve for x and y, 3x + iy = (1 + i)(x^2 + y^2). Ans: x = 3/10 and y = 9/10 \n" ); document.write( "

Algebra.Com's Answer #728756 by math_helper(2461) $\"\"$ $\"About$

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$\"+3x+%2B+yi+=+%281%2Bi%29%28x%5E2%2By%5E2%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "Let $\"+k=x%5E2%2By%5E2+\"$ for now:\r
\n" ); document.write( "\n" ); document.write( " $\"++3x%2Byi+=+%281%2Bi%29k+\"$
\n" ); document.write( " $\"++3x%2Byi+=+k%2Bki+\"$
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\n" ); document.write( "\n" ); document.write( "Using Re{LHS} = Re{RHS}, Im{LHS}=Im{RHS} :
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document.write( "3x = k  —>  x = k/3  (1)\r\n" );
document.write( "y = k                (2) 
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\n" ); document.write( "\n" ); document.write( "But $\"+x%5E2%2By%5E2+=+k+\"$ so, using (1) and (2):
\n" ); document.write( " $\"+k%5E2%2F9+%2B+k%5E2++=+k+\"$
\n" ); document.write( " $\"++10k%5E2+-+9k+=+0+\"$
\n" ); document.write( "k=0 and/or k=9/10\r
\n" ); document.write( "\n" ); document.write( "k=0 is a trivial solution (x=y=k=0)
\n" ); document.write( "k=9/10 —> $\"+highlight%28+x+=+3%2F10%29+\"$ , $\"+highlight%28++y+=+9%2F10%29+\"$ \n" ); document.write( "

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