document.write( "Question 859033: Find the value of X and Y from the given equation : sqrt(X)+Y=7 & sqrt(Y)+X=11 \n" ); document.write( "

Algebra.Com's Answer #517510 by Fombitz(32388) $\"\"$ $\"About$

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Use a substitution, $\"u=sqrt%28x%29\"$ , $\"u%5E2=x\"$ , $\"v=sqrt%28y%29\"$ , $\"v%5E2=y\"$
\n" ); document.write( "1. $\"u%2Bv%5E2=7\"$
\n" ); document.write( "2. $\"v%2Bu%5E2=11\"$
\n" ); document.write( "From eq. 1,
\n" ); document.write( " $\"u=7-u%5E2\"$
\n" ); document.write( " $\"u%5E2=49-14v%5E2%2Bv%5E4\"$
\n" ); document.write( "Substitute into eq. 2,
\n" ); document.write( " $\"v%2B49-14v%5E2%2Bv%5E4=11\"$
\n" ); document.write( " $\"v%5E4-14v%5E2%2Bv%2B38=0\"$
\n" ); document.write( " $\"%28v-2%29%28v%5E3%2B2v%5E2-10v-19%29=0\"$
\n" ); document.write( "Unfortunately the cubic cannot be factored any further.
\n" ); document.write( "You need to use numerical methods to find the roots.
\n" ); document.write( " $\"v=-3.28\"$
\n" ); document.write( " $\"v=-1.85\"$
\n" ); document.write( " $\"v=3.13\"$
\n" ); document.write( "and from above
\n" ); document.write( " $\"v=2\"$
\n" ); document.write( "We need to verify that each of these are actual solutions.
\n" ); document.write( " $\"sqrt%28y%29=2\"$
\n" ); document.write( " $\"y=4\"$
\n" ); document.write( "and
\n" ); document.write( " $\"sqrt%28x%29%2B4=7\"$
\n" ); document.write( " $\"sqrt%28x%29=3\"$
\n" ); document.write( " $\"x=9\"$
\n" ); document.write( "Verifying,
\n" ); document.write( " $\"x%2Bsqrt%28y%29=11\"$
\n" ); document.write( " $\"9%2Bsqrt%284%29=11\"$
\n" ); document.write( " $\"9%2B2=11\"$
\n" ); document.write( " $\"11=11\"$
\n" ); document.write( "True, good solution is $\"x=9\"$ , $\"y=4\"$
\n" ); document.write( "Next,
\n" ); document.write( " $\"v=3.13\"$
\n" ); document.write( " $\"sqrt%28y%29=3.13\"$
\n" ); document.write( " $\"y=9.797\"$
\n" ); document.write( " $\"sqrt%28x%29%2B9.797=7\"$
\n" ); document.write( " $\"sqrt%28x%29=-2.797\"$
\n" ); document.write( "Doesn't lead to a valid solution.
\n" ); document.write( "Same for the other two possible solutions.
\n" ); document.write( "Only one solution.
\n" ); document.write( " \n" ); document.write( "

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