document.write( "Question 826730: how do you find the real number of x^4+5x^2=6 \n" ); document.write( "

Algebra.Com's Answer #498255 by KMST(5328) $\"\"$ $\"About$

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ONE WAY:
\n" ); document.write( "Rename $\"x%5E2=y\"$ to get $\"y%5E2%2B5y=6\"$ <--> $\"y%5E2%2B5y-6=0\"$ , then solve.
\n" ); document.write( "That change of variable turns the problem into an easier one, where you may clearly see the solution.
\n" ); document.write( "Factoring, you transform $\"y%5E2%2B5y-6=0\"$
\n" ); document.write( "into $\"%28y%2B6%29%28y-1%29=0\"$ ,
\n" ); document.write( "which has the solutions $\"y=-6\"$ and $\"y=1\"$ .
\n" ); document.write( "From $\"y=1\"$ you get $\"x%5E2=1\"$ with real solutions
\n" ); document.write( " $\"highlight%28x=1%29\"$ and $\"highlight%28x=-1%29\"$ .
\n" ); document.write( "You cannot get real solutions from $\"y=-6\"$ --> $\"x%5E2=-6\"$ .
\n" ); document.write( "
\n" ); document.write( "ANOTHER WAY:
\n" ); document.write( "Just say that you are factoring, like this
\n" ); document.write( " $\"x%5E4%2B5x%5E2=6\"$
\n" ); document.write( " $\"x%5E4%2B5x%5E2-6=0\"$
\n" ); document.write( " $\"%28x%5E2%2B6%29%28x%5E2-1%29=0\"$
\n" ); document.write( " $\"x%5E2%2B6%29%28x%2B1%29%28x-1%29=0\"$
\n" ); document.write( "where $\"x%5E2%2B6%3E=6%3E0\"$ for all $\"x\"$ ,
\n" ); document.write( "and the other factors' zeros,
\n" ); document.write( " $\"highlight%28x=1%29\"$ and $\"highlight%28x=-1%29\"$ ,
\n" ); document.write( "are the only real solutions. \n" ); document.write( "

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