document.write( "Question 985922: y=x^2-10
\n" ); document.write( "9x^2-y^2=90
\n" ); document.write( "The solution set is? \n" ); document.write( "

Algebra.Com's Answer #606728 by MathLover1(20855) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"y=x%5E2-10\"$
\n" ); document.write( " $\"9x%5E2-y%5E2=90\"$
\n" ); document.write( "----------------\r
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-10\"$
\n" ); document.write( " $\"9x%5E2-90=y%5E2\"$
\n" ); document.write( "----------------\r
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-10\"$
\n" ); document.write( " $\"y=sqrt%289x%5E2-90%29\"$
\n" ); document.write( "----------------\r
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-10\"$
\n" ); document.write( " $\"y=sqrt%289%28x%5E2-10%29%29\"$
\n" ); document.write( "----------------\r
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-10\"$
\n" ); document.write( " $\"y=3sqrt%28x%5E2-10%29\"$
\n" ); document.write( "----------------\r
\n" ); document.write( "\n" ); document.write( "if left sides same, then we have\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2-10=3sqrt%28x%5E2-10%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%2F3-10%2F3=sqrt%28x%5E2-10%29\"$ ............square both sides\r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2F3-10%2F3%29%5E2=%28sqrt%28x%5E2-10%29%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2%2F3%29%5E2-2%28x%5E2%2F3%29%2A%28-10%2F3%29%2B%28-10%2F3%29%5E2=x%5E2-10\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E4%2F9%29-%2820x%5E2%2F9%29%2B%28100%2F9%29=x%5E2-10\"$ .....both sides multiply by $\"9\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"9%28x%5E4%2F9%29-9%2820x%5E2%2F9%29%2B9%28100%2F9%29=9x%5E2-90\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E4-20x%5E2%2B100=9x%5E2-90\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E4-20x%5E2%2B100-9x%5E2%2B90=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E4-29x%5E2%2B190=0\"$ ....factor\r
\n" ); document.write( "\n" ); document.write( " $\"x%5E4-19x%5E2-10x%5E2%2B190=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E4-19x%5E2%29-%2810x%5E2-190%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x%5E2%28x%5E2-19%29-10%28x%5E2-19%29=0\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28x%5E2-19%29%28x%5E2-10%29+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( "zeros:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "if $\"x%5E2-19+=+0\"$ => $\"x%5E2=19+\"$ => $\"x=sqrt%2819%29+\"$ or $\"x=-sqrt%2819%29+\"$
\n" ); document.write( "if $\"x%5E2-10+=+0\"$ => $\"x%5E2=10+\"$ => $\"x=sqrt%2810%29+\"$ or $\"x=-sqrt%2810%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "approximately:\r
\n" ); document.write( "\n" ); document.write( " $\"x=4.4+\"$ or $\"x=-4.4+\"$
\n" ); document.write( " $\"x=3.2+\"$ or $\"x=-3.2+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-10\"$
\n" ); document.write( " $\"9x%5E2-y%5E2=90\"$ \r
\n" ); document.write( "\n" ); document.write( "for $\"x+=+sqrt%2819%29\"$ => $\"y=%28sqrt%2819%29%29%5E2-10\"$ => $\"y=19-10\"$ => $\"y+=+9\"$
\n" ); document.write( "for $\"x+=+sqrt%2810%29\"$ => $\"y=%28sqrt%2810%29%29%5E2-10\"$ => $\"y=10-10\"$ => $\"y+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( "for $\"x+=+sqrt%2819%29\"$ => $\"9%28sqrt%2819%29%29%5E2-90=y%5E2\"$ => $\"171-90=y%5E2\"$ => $\"81=y%5E2\"$ => $\"y+=+9\"$ and => $\"y+=+-9\"$ \r
\n" ); document.write( "\n" ); document.write( "for $\"x+=+sqrt%2810%29\"$ => $\"9%28sqrt%2810%29%29%5E2-90=y%5E2\"$ => $\"90-90=y%5E2\"$ => $\"9=y%5E2\"$ => $\"y+=+0\"$ \r
\n" ); document.write( "\n" ); document.write( "check:\r
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