Answer:
Step-by-step explanation:
Appropriate math notation and parentheses would help immensely. As written, neither of these questions makes any sense.
1.
[tex]-8\sqrt[5]{19x+15}=-24\qquad\text{seems like what you may mean}\\\\\sqrt[5]{19x+15}=3\qquad\text{divide by -8}\\\\19x+15=3^5=243\qquad\text{raise to the 5th power}\\\\19x=228\qquad\text{subtract 15}\\\\x=12\qquad\text{divide by 19}[/tex]
The solution is x=12.
2.
Square both sides of the equation:
... 2x -7 -2√(x(2x-7)) +x = 1
... 3x -8 = 2√(x(2x -7)) . . . . add 2√(x(2x-7)) -1
... 9x² -48x +64 = 4(2x² -7x) . . . . square both sides of the equation again
... x² -20x +64 = 0 . . . . add -8x²+28x
... (x -4)(x -16) = 0 . . . . factor the equation (one of many ways to find its roots)
... x = 4 or x = 16 . . . . values of x that make the factors 0
Try the solution x=4:
... √(2·4-7) -√4 = 1 - 2 ≠ 1 . . . . . not a solution
Try the solution x=16:
... √(2·16-7) -√16 = 5 -4 = 1 . . . . . is a solution
The only solution is x=16.
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Comment on the graph
Each of the equations has been recast to be of the form f(x) = 0, by adding the opposite of the right side of the equal sign. The graphing calculator highlights the zeros, so highlights the solution to the equation. You can see that the second equation (green graph) has only one solution.
