How do you solve sqrt(20-n)+8=sqrt(9-n)+11?

2 Answers
Tony B
Oct 16, 2016

n=80/9

Explanation:

Given:" "sqrt(20-n)+8=sqrt(9-n)+11

color(brown)("When ever you have roots try and get rid of them. This may not always work")

Subtract 8 from both sides isolating one of the roots.

" "sqrt(20-n)=sqrt(9-n)+3

Square both sides

20cancel(-n)=[9cancel(-n)] + 6sqrt(9-n)+9

Subtract 18 from both sides (9+9=18)

2=6sqrt(9-n)

Divide both sides by 6

1/3=sqrt(9-n)

Square both sides

1/9=9-n

n=80/9
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
color(blue)("Check") comparing left to right

sqrt(20-n)+8->sqrt(9-n)+11

sqrt(20-80/9)+8->sqrt(9-80/9)+11

sqrt(100/9)+8->sqrt(1/9)+11

10/3+8->1/3+11

34/3->34/3 Thus LHS = RHS ->color(red)(" True")

P dilip_k
Dec 7, 2016

sqrt(20-n)+8=sqrt(9-n)+11

=>sqrt(20-n)-sqrt(9-n)=11-8

=>sqrt(20-n)-sqrt(9-n)=3.... .[1]

=>1/(sqrt(20-n)-sqrt(9-n))=1/3

=>(sqrt(20-n)+sqrt(9-n))/(20-n-9+n)=1/3

=>(sqrt(20-n)+sqrt(9-n))/11=1/3

=>(sqrt(20-n)+sqrt(9-n))= 11/3......[2]

Adding [1] and [2] we get

2sqrt(20-n)=3+11/3=20/3

=>sqrt(20-n)=10/3

=>(20-n)=100/9

=>n=20-100/9=80/9

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