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Solve `3+sqrt(z-6)=sqrt(z+9)` :
`3+sqrt(z-6)=sqrt(z+9)` square both sides
`sqrt(z-6)=1` square both sides
Since we squared, we must check that z=7 is not an extraneous solution. `3+sqrt(7-6)=4=sqrt(7+9)` checks.
The solution is z=7.
The graphs of `y=3+sqrt(z-6)` and `y=sqrt(z+9)` :
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