document.write( "Question 926377: please help me solve this equation
\n" ); document.write( " x^2+2xy−y^2=−17
\n" ); document.write( " x^2−y^2=−45 \n" ); document.write( "

Algebra.Com's Answer #562209 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x%5E2%2B2xy-y%5E2=-17\"$ ..........eq.1
\n" ); document.write( " $\"+x%5E2-y%5E2=-45\"$ ..........eq.2
\n" ); document.write( "_____________________________________subtract eq.2 from eq.1\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2B2xy-y%5E2-%28x%5E2-y%5E2%29=-17-%28-45%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"cross%28x%5E2%29%2B2xy-cross%28y%5E2%29-cross%28x%5E2%29%2Bcross%28y%5E2%29=-17%2B45\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"2xy+=28\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"xy+=14\"$ .....solve for $\"x\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x+=14%2Fy\"$ .....eq.1a\r
\n" ); document.write( "\n" ); document.write( "go to $\"+x%5E2-y%5E2=-45\"$ ..........eq.2, substitute $\"x+=14%2Fy\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"+%2814%2Fy%29%5E2-y%5E2=-45\"$ ....solve for $\"y\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"+14%5E2%2Fy%5E2-y%5E2=-45\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+196%2Fy%5E2=y%5E2-45\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"196=y%5E2%28y%5E2-45%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"196=y%5E4-45y%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"0=y%5E4-45y%5E2-196\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y%5E4%2B2y%5E2-49y%5E2-196=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28y%5E4%2B2y%5E2%29-%2849y%5E2%2B196%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y%5E2%28y%5E4%2B2%29-49%28y%5E2%2B4%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28y%5E2-49%29%28y%5E2%2B4%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28y%5E2-7%5E2%29%28y%5E2%2B4%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28y-7%29%28y%2B7%29%28y%5E2%2B4%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( "if $\"y-7=0\"$ => $\"y=7\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"y%2B7=0\"$ => $\"y=-7\"$ \r
\n" ); document.write( "\n" ); document.write( "if $\"y%5E2%2B4=0\"$ => $\"y%5E2=-4\"$ => $\"y=sqrt%28-4%29\"$ => $\"y=2i\"$ or $\"y=-2i\"$ ; complex solutions\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so, $\"x+=14%2Fy\"$ will be\r
\n" ); document.write( "\n" ); document.write( "real solutions:\r
\n" ); document.write( "\n" ); document.write( " $\"x+=14%2F7\"$ => $\"x+=2\"$ if $\"y=7\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x+=14%2F-7\"$ => $\"x+=-2\"$ if $\"y=-7\"$ \r
\n" ); document.write( "\n" ); document.write( "complex solutions: \r
\n" ); document.write( "\n" ); document.write( " $\"x+=14%2F2i\"$ => $\"x+=7i\"$ if $\"y=2i\"$
\n" ); document.write( "and
\n" ); document.write( " $\"x+=14%2F-2i\"$ => $\"x+=-7i\"$ if $\"y=-2i\"$ \r
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