Solving radical equations 3 + radicand z-6 = radicand z+9.

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Solve `3+sqrt(z-6)=sqrt(z+9)` :

`3+sqrt(z-6)=sqrt(z+9)` square both sides

`9+6sqrt(z-6)+z-6=z+9`

`6sqrt(z-6)=6`

`sqrt(z-6)=1` square both sides

`z-6=1`

z=7

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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