example 8-1a
DESCRIPTION
Solve. Original equation. Add 1 to each side to isolate the radical. Square each side to eliminate the radical. Find the squares. Add 2 to each side. Example 8-1a. Original equation. Replace y with 38. Simplify. Example 8-1b. Check. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/1.jpg)
Solve
Original equation
Add 1 to each side to isolate the radical.
Square each side to eliminate the radical.
Find the squares.
Add 2 to each side.
![Page 2: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/2.jpg)
Check
Answer: The solution checks. The solution is 38.
Replace y with 38.
Original equation
Simplify.
![Page 3: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/3.jpg)
Answer: 67
Solve
![Page 4: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/4.jpg)
Solve
Original equation
Square each side.
Find the squares.
Isolate the radical.
Divide each side by –4.
![Page 5: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/5.jpg)
Answer: The solution does not check, so there is no real solution.
Check
Square each side.
Evaluate the squares.
Original equation
Evaluate the square roots.
Replace x with 16.
Simplify.
![Page 6: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/6.jpg)
Solve .
Answer: no real solution
![Page 7: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/7.jpg)
Solve
In order to remove the power, or cube root, you must
first isolate it and then raise each side of the equation to
the third power.
Original equation
Subtract 5 from each side.
Cube each side.
Evaluate the cubes.
![Page 8: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/8.jpg)
Answer: The solution is –42.
Divide each side by 3. Check
Original equation
Add.
Replace y with –42.
Simplify.
The cube root of –125 is –5.
Subtract 1 from each side.
![Page 9: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/9.jpg)
Answer: 13
Solve
![Page 10: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/10.jpg)
Solve
Since the radicand of a square root must be greater than or equal to zero, first solve to identify the values of x for which the left side of the inequality is defined.
![Page 11: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/11.jpg)
Now solve .
Original inequality
Isolate the radical.
Eliminate the radical.
Add 6 to each side.
Divide each side by 3.
Answer: The solution is
![Page 12: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/12.jpg)
CheckTest some x values to confirm the solution. Let
Use three test values: one less than 2, one between 2 and 5, and one greater than 5.
Only the values in the intervalsatisfy the inequality.
Since is not a real number, the inequality is not satisfied.
Since the inequality is satisfied.
Sincethe inequality is not satisfied.
![Page 13: Example 8-1a](https://reader036.vdocument.in/reader036/viewer/2022071718/56813324550346895d9a0449/html5/thumbnails/13.jpg)
Answer:
Solve