Transcript Solve and Check!

Section 7.6
Solving Radical Equations
x2  4
3
3x  1  5 x  9
x  1
2
Key Ideas
How do you:
Un-Square Something?  Square-Root it!
Un Cube Something?  Cube-Root it!
Un-Square-Root Something?  Square it!
Un Cube-Root Something?  Cube it!
If you do something to one side of the equation,
you have to do that to the other side.
When solving equations, you have to undo the
order of operations in the opposite order.
Solve and Check!
x2  4
We have to get rid of the square root, so
we square both sides.


x  2  4
2
2
On the left, the square-root and square, cancel out.
x  2  16
Add 2 to both sides.
Don’t forget to check!
18  2  4
x  18
16  4
Solve and Check!
2 x  3  2  0 Add 2 to both sides.
2x  3  2


2 x  3  2 
2x  1
2
2
1
x
2
Square both sides.
2x  3  4
Don’t forget
to check!
Subtract 3.
1
2   3  2  0
 2
Solve and Check!
5 x  1  4  4


5 x  1   8
2
5 x  1  8
5x 1  64
2
Don’t forget
to check!
5x  65
x  13
513 1  4  4
65  1  4  4
8  4  4
12  4
64  4  4
That’s not true!
What does this mean?
A solution that doesn’t check is called
an “extraneous solution.”
Therefore, the equation we started with
has no solutions. Why?
We did all the math correctly, but when
we checked our solution, it didn’t work.
You Try One!
Solve and Check!
2x  1 1  3
Try Another One!
Solve and Check
2 x  1  3x  8
Last One for Now!
Solve and Check
3
x  1
2