document.write( "Question 4919: I need some help please: Solve the following equations: A) sqr(x+1)= 5- sqr(x-4) and B) sqr(x-2)=sqr(x+7)-1 and C) sqr(2n-1) + sqr(n-5) = 3
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Algebra.Com's Answer #3263 by guapa(62) $\"\"$ $\"About$

You can put this solution on YOUR website!
These radical equations you solve by using the following property of equality:
\n" ); document.write( "For all real numbers a and b, if a=b, then $\"a%5E2=b%5E2\"$
\n" ); document.write( "A)
\n" ); document.write( " $\"sqrt%28x%2B1%29=5-sqrt%28x-4%29\"$ Now square both sides
\n" ); document.write( " $\"sqrt%28x%2B1%29%5E2=%285-sqrt%28x-4%29%29%5E2\"$
\n" ); document.write( "Let's look at each side seperately since it becomes kind of messy.
\n" ); document.write( " $\"sqrt%28x%2B1%29%5E2\"$ = $\"x%2B1\"$
\n" ); document.write( "For the right side:
\n" ); document.write( " $\"%285-sqrt%28x-4%29%29%285-sqrt%28x-4%29%29\"$ = $\"25-5sqrt%28x-4%29-5sqrt%28x-4%29%2B%28x-4%29\"$ =
\n" ); document.write( " $\"25-10sqrt%28x-4%29%2Bx%2B4\"$ = $\"x%2B21-10sqrt%28x-4%29\"$
\n" ); document.write( "Thus we get:
\n" ); document.write( " $\"x%2B1=x%2B21-10sqrt%28x-4%29\"$
\n" ); document.write( "Add x to and substract 21 from both sides
\n" ); document.write( " $\"20=-10sqrt%28x-4%29\"$
\n" ); document.write( "Divide both sides by -10
\n" ); document.write( " $\"-2=sqrt%28x-4%29\"$ Again square both sides
\n" ); document.write( " $\"4=x-4\"$ Add 4 to both sides
\n" ); document.write( " $\"x=8\"$
\n" ); document.write( "For the next 2 you proceed the same pattern\r
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