SOLUTION: Please help me solve this equation, I keep coming up with the wrong answer: {{{sqrt(n-4)+ sqrt(n+4)=2sqrt(n-1)}}}

Algebra ->  Radicals -> SOLUTION: Please help me solve this equation, I keep coming up with the wrong answer: {{{sqrt(n-4)+ sqrt(n+4)=2sqrt(n-1)}}}      Log On


   

Question 57614This question is from textbook Elementary and Intermediate Algebra
: Please help me solve this equation, I keep coming up with the wrong answer:
sqrt%28n-4%29%2B+sqrt%28n%2B4%29=2sqrt%28n-1%29 This question is from textbook Elementary and Intermediate Algebra

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28n-4%29%2B+sqrt%28n%2B4%29=2sqrt%28n-1%29
%28sqrt%28n-4%29%2Bsqrt%28n%2B4%29%29%5E2=%282sqrt%28n-1%29%29%5E2


%28n-4%29%2B2sqrt%28%28n%2B4%29%28n-4%29%29%2B%28n%2B4%29=4n-4
2n-4%2B4%2B2sqrt%28n%5E2-16%29=4n-4
2n%2B2sqrt%28n%5E2-16%29=4n-4
2n-2n%2B2sqrt%28n%5E2-16%29=4n-2n-4
2sqrt%28n%5E2-16%29=2n-4
2sqrt%28n%5E2-16%29%2F2=2n%2F2-4%2F2
sqrt%28n%5E2-16%29=n-2
%28sqrt%28n%5E2-16%29%29%5E2=%28n-2%29%5E2
n%5E2-16=n%5E2-4n%2B4
n%5E2-n%5E2-16=n%5E2-n%5E2-4n%2B4
-16=-4n%2B4
-16-4=-4n%2B4-4
-20=-4n
-20%2F-4=-4n%2F-4
5=n
:
Yopu must always check these kinds of equations for extraneous solutions by subtituting 5 in for n in the original equation.
sqrt%285-4%29%2Bsqrt%285%2B4%29=2%2Asqrt%285-1%29
sqrt%281%29%2Bsqrt%289%29=2%2Asqrt%284%29
1%2B3=2%2A2
4=4 We've got a solution!!!
highlight%28n=5%29
Happy Calculating!!!